Permutations and Combinations

1. Permutations and Combinations

2. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

3. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

4. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

5. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

6. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

7. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

8. Permutations and Combinations Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA Think of a permutation as “all possible ways of doing something”

9. Permutations and Combinations Example # 2 : An airline company has to fill 2 pilot positions and it has 15 candidates to choose from. How many different ways can the positions be filled ?

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14. Permutations and Combinations Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ?

15. Permutations and Combinations Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ? Let’s try the shortcut … n = 18 r = 5 So I am going to start to count down from 18 and take the first 5 numbers…

16. Permutations and Combinations Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ? Let’s try the shortcut … n = 18 r = 5 So I am going to start to count down from 18 and take the first 5 numbers…

17. Permutations and Combinations Combination – kind of like a permutation but the order doesn’t matter. Example : How many combinations of flavors can I choose if I am getting 3 scoops of ice cream and there are 10 flavors available ? Let’s say I choose chocolate, vanilla, and strawberry. The order doesn’t matter, I could order vanilla, strawberry, and chocolate.

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24. Permutations and Combinations Let’s try the shortcut in this example : There are 15 freshman trying out for the swim team. The coach can only choose 6 of them. How many different 6 member squads can the coach select ?

25. Permutations and Combinations Let’s try the shortcut in this example : There are 15 freshman trying out for the swim team. The coach can only choose 6 of them. How many different 6 member squads can the coach select ? n = 15 r = 6 Count down from 15 for 6 numbers and divide by r!

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