10.3 – 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. 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 important? (AB, AC, BC, BA, CA, CB) 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. c) 6 P 6 a) 5 P 3 b) 5 C 3 d) 6 C 6 54354
10.3 – 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: 2. Determine the set of three digits.1. Determine the set of two letters. 26 P 210 P 3 26 9 ,000
10.3 – 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
10.3 – 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}. 9C39C3 84 Different subsets 9P39P3 987987 504arrangements
10.3 – Using Permutations and Combinations Guidelines on Which Method to Use