Using Permutations and Combinations Permutation The number of
Using Permutations and Combinations Permutation: The number of ways in which a subset of objects can be selected from a given set of objects, where order is important. Given the set of three letters, {A, B, C}, how many possibilities are there for selecting any two letters where order is important? (AB, AC, BA, CB) Combination: The number of ways in which a subset of objects can be selected from a given set of objects, where order is not important. Given the set of three letters, {A, B, C}, how many possibilities are there for selecting any two letters where order is not important? (AB, AC, BC).
10. 3 – Using Permutations and Combinations Factorial Formula for Permutations Factorial Formula for Combinations
10. 3 – Using Permutations and Combinations Evaluate each problem. b) 5 C 3 c) 6 P 6 d) 6 C 6 a) 5 P 3 5 4 3 60 10 720 1
Using Permutations and Combinations How many ways can you select two letters followed by three digits for an ID if repeats are not allowed? Two parts: 1. Determine the set of two letters. 2. Determine the set of three digits. 26 P 2 10 P 3 26 25 10 9 8 650 720 468, 000
Using Permutations and Combinations A common form of poker involves hands (sets) of five cards each, dealt from a deck consisting of 52 different cards. How many different 5 -card hands are possible? Hint: Repetitions are not allowed and order is not important. 52 C 5 2, 598, 960 5 -card hands
Using Permutations and Combinations Find the number of different subsets of size 3 in the set: {m, a, t, h, r, o, c, k, s}. Find the number of arrangements of size 3 in the set: {m, a, t, h, r, o, c, k, s}. 9 C 3 9 P 3 9 8 7 504 84 Different subsets arrangements
Using Permutations and Combinations Guidelines on Which Method to Use
Other Permutations • Permutations with Repeats n!/k! k=number of copies/repeats How many ways can the letters in MISSISSIPPI be arranged • Circular Permutations (n-1)! If there are 8 people dancing in a circle at Maddy’s wedding reception, how many different ways can they be arranged?
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