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Permutation

Permutation. A permutation is an arrangement in which order matters. A B C differs from B C A. How Many Permutations?. Consider four objects {A,B,C,D} There are 4 choices for the first slot. There are 3 choices for the second slot. There are 2 choices for the third slot.

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Permutation

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  1. Permutation A permutation is an arrangement in which order matters. A B C differs from B C A

  2. How Many Permutations? Consider four objects {A,B,C,D} There are 4 choices for the first slot. There are 3 choices for the second slot. There are 2 choices for the third slot. There is 1 choice for the last slot.

  3. 4 x 3 x 2 x 1 = 24 Permutations ABCD ABDC ACBD ACDB ADBC ADCB BACD BADC BCAD BCDA BDAC BDCA CABD CADB CBAD CBDA CDAB CDBA DABC DACB DBAC DBCA DCAB DCBA

  4. Generalization There are 4! ways to arrange 4 items. There are n! ways to arrange n items.

  5. Permutation Formula In how many ways may r items be selected out of a set of n items where order matters

  6. Permutation Example Selecting 3 items out of a set of 5 We have 5 choices for the first item. We have 4 choices for the second item. We have 2 choices for the third item. 5 x 4 x 3 = 60 Permutations

  7. Calculations

  8. Permutation Formula

  9. Combinations Combinations are arrangements in which order does NOT matter. A, B, C is the same as B, C, A

  10. Evaluating In how many ways may 3 items be selected from a set of 5 without regard to order?

  11. We already know that there 60permutations of these items. For each set of three, there are 3! or 6 arrangements. A B C A C B B A C B C A C A B C B A All of these are really the same.

  12. Our actual answer is 10. Consider the set {A,B,C,D,E} These are the combinations. A,B,C A,B,D A,B,E A,C,D A,C,E A,D,E B,C,D B,C,E B,D,E C,D,E

  13. Combination Formula

  14. Lottery Calculations In a lottery, 5 winning numbers are selected out of a set of 15 numbers. How many possibilities?

  15. What is your probability? You are likely to win one game out of 3003 games. Hot Diggety Dog!

  16. Selecting Exactly 4 Winners(This actually means 4 of the 5 correct numbers and one of the 15 incorrect numbers.)

  17. Selecting Exactly 3 Winners Here is your opportunity to shine. Calculate it yourself!

  18. Check Your Answer If you got this answer, smile and pat yourself on the back.

  19. There’s no place like home! Click to Return

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