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## MATH 110 Sec 12.1 Intro to Counting Practice Exercises

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**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear?**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,,**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, .**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . He still has 4choices of pants**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . He still has 4choices of pants And for eachchoice of pants, he has 6 choices of jackets**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . He still has 4choices of pants So, the designer has 24 different outfits that include top, . And for eachchoice of pants, he has 6 choices of jackets**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top,**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, But the designer does not have to stick with Top, .**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, If he decided to use Top, instead, there would be another 24 different outfits.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, If he decided to use Top, instead, there would be another 24 different outfits.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, If he decided to use Top, , there would be another 24 different outfits.**X**MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, If he decided to use Top, , there would be another 24 different outfits.**X**MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, If he decided to use Top, , there would be another 24 different outfits.**X**X MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, If he decided to use Top, , there would be another 24 different outfits.**X**MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, Finally, if he decided to use Top, , there would be another 24 different outfits.**X**X MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, Finally, if he decided to use Top, , there would be another 24 different outfits.**X**X MATH 110 Sec 12.1 Intro to Counting Practice Exercises X X X X A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? ,, Suppose the designer has already decided to use the Top, . So, all together, there would be 24 x 5 = 120 different possible outfits. So, the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, and the designer has 24 different outfits that include top, Finally, if he decided to use Top, , there would be another 24 different outfits.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. Note: Because we also covered the section on the Fundamental Counting Principle, we could actually use that to answer this question much more efficiently.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**A designer designed 5 different tops, 4 different pants and6 different jackets. How many different outfits (consisting of 1 top, 1 pair of pants & 1 jacket) can the model possibly wear? So the model could possibly wear 120 different outfits. THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways. Notice that you get the same answer as before without having to draw a tree diagram.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription?**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? Because a tree diagram here would be very large, we will once again take advantage of the fact that we have already covered the section on the Fundamental Counting Principle.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways. Here we will be choosing from 4 possible letters (U, V, E, A) and 3 possible numbers (8, 3, 7).**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)A task composed of a series of sub-tasks in which the first sub-task can be performed in a ways, the second in b ways, thethirdincways,andsoon,canbedoneinaxbxcx ... ways.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**An eyewitness to a crime said that the license plate of the getaway car began with the four letters U, V, E and A (but he couldn’t remember the order). The rest of the plate had the numbers 8, 3 and 7 but, again, he could not remember the order. Howmanylicenseplatesfittheeyewitnessdescription? 144 license plates fit the eyewitness description.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together?**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? To make it easier to see how to keep the 2 males apart, let’s replace the male names with & and the female names with and .**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? To make it easier to see how to keep the 2 males apart, let’s replace the male names with & and the female names with and .**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? Our task is to list every possible way that the couples could be seated without the men sitting together.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? Suppose sits in the first seat.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? Suppose sits in the first seat. We can’t seat in seat 2 but we can seat either or there.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? Suppose sits in the first seat. We can’t seat in seat 2 but we can seat either or there.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? If sits in the first seat and sits in the second seat, then either of the two remaining ( or ) can be next.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? If sits in the first seat and sits in the second seat, then either of the two remaining ( or ) can be next.**MATH 110 Sec 12.1 Intro to Counting Practice Exercises**Two couples (Adam/Brenda and Carl/Darlene) bought tickets to a musical. In how many ways can the couples be seated if the men do not sit together? If sits in the first seat and sits in the second seat, then either of the two remaining ( or ) can be next.