I CAN: Use Permutations and Combinations Chapter 1 Section 11-3 I CAN: Use Permutations and Combinations

Guidelines on Which Method to Use Permutations Combinations Order matters! Order doesn’t matter! Arrangements of n items taken r at a time Subsets of n items taken r at a time Clue words: arrangement, schedule, order, rank, holding offices (Pres), rearranging numbers Clue words: group, sample, selection, committee

Factorial Formula for Permutations Arrangements are called permutations The number of permuations of n things taken r at a time is denoted as: n = _________________ r = _________________ n must be greater than r ORDER MATTERS *Can’t have more #s in a subset than the total # of items!

Example: Permutations Evaluate each permutation. 5P3 b) 10P4

Example: IDs How many ways can you select two letters followed by three digits for an ID if repeats are NOT allowed? TWO PARTS!!   …or how did we do this question in 11.2? ___ ___ ___ ___ ___

Example: Building Numbers From a Set of Digits How many four-digit numbers can be written using the numbers from the set {1, 3, 5, 7, 9} if repetitions are not allowed?  

Factorial Formula for Combinations In counting problems, subsets where the order of the elements makes no difference are called Combinations: The # of combinations of n things taken r at a time *ORDER DOES NOT MATTER*

Example: Combinations Evaluate each combination. 5C3 b) 7C2

Example: Finding the Number of Subsets Find the number of different subsets of size 3 in the set {m, a, t, h, r, o, c, k, s}.  

Example: Finding the Number of Poker Hands 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? Repetitions are not allowed and order is not important.  

Example: Forming Committees A city council has 8 members. The council needs to set up a committee of 5 for a zoning issue. In how many ways can a committee be selected?  

11.3 Book Work p. 702 #1-15 odd, 19-27 odd (skipping 17), 37, 53