12.3 Permutations and Combinations

12.3 Permutations and Combinations

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12.3 Permutations and Combinations

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1. 12.3 Permutations and Combinations Mrs. Taormina Probability and Statistics

2. Permutationsand Combinations

3. What’s the Difference? "My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. (order does not matter) Combination

4. What’s the Difference? "The combination to the safe was 472". Now we do care about the order. "724" would not work, nor would "247". It has to be exactly 4-7-2. (Order matters) Permutation This should be called a “permutation” lock! (You can laugh…ha! ha!)

5. Factorial ! 7 ! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 3 ! = 3 x 2 x 1 = 6 On Calculator: MATH PRB ! (#4)

6. Permutations • This formula is used for permutations without repetition. (The FCP took care of repetition). How many we are choosing Number of items

7. Combinations • This formula is used for combinations without repetition. How many we are choosing at a time Number of items

8. Pascal’s Triangle C(0, 0)=1 C(1, 0)=1 C(1,1)=1 C(2, 0)=1 C(2,1)=2 C(2,2)=1 C(3, __) etc. C(4, __) C(5, __)

9. ASSIGNMENT: Pg. 708 #7-56 (Tuesday and Wednesday) Calculator Steps: Enter n MATH PRB (#2-nPr) or (#3-nCr) enter r Today at 2:00 p.m. we will be having a tornado drill. Our class must sit together in the science hallway. (Single row, sitting towards the wall, not in front of glass, with your head covered)