Day 5 examples
- 1. Combinations A set or collection of things in no particular order In permutations: ORDER MATTERS In combinations: Order does NOT matter In general, the number of combinations of "n" things taken or chosen "r" at a time nCr = n! Reads "n choose r" (n - r)! r! Perms: Combs: Phone numbers VS. Card hands Locker Combinations Lottery Numbers License Plates Committees
- 2. Ex) In how many ways can a committee of 4 be chosen from 4 teachers and 3 students if (a) all are equally eligible? (b) the committee must include 2 teachers AND 2 students?
- 3. Ex) From a group of 5 students, 3 will be chosen to work on a grad committee. (a) How many different committees of 3 are possible? (b) If Amanda, one of the students, has to be on the committee, how many are possible?
- 4. Ex) A cribbage hand consists of 6 cards (a) How many different hands are possible? (b) How many hands with 3 kings only are possible? (c) How many hands with 2 or more kings?
- 5. Ex) A class has 15 girls and 20 boys. (a) How many committees of eight consisting of 3 girls and 5 boys can be made? (b) If Jill, Melissa, and Adam must be on the committee? (c) A committee of 5 with at least 3 girls?