Section 6.4

1. Section 6.4 Permutations and Combinations

2. Permutations A permutation of a set of objects is an arrangement of these objects in a definite order. Combinations A combination is a selection of r objects from a set of n objects where order is not important

3. n–Factorial For any natural number n, Ex. 5! = 5(4)(3)(2)(1) = 120 Ex. This notation allows us to write expressions associated with permutations and combinations in a compact form.

4. Permutations of n Distinct Objects The number of permutations of n distinct objects taken r at a time is given by Ex.

5. Ex. A boy has 4 beads – red, white, blue, and yellow. How different ways can three of the beads be strung together in a row? This is a permutation since the beads will be in a row (order). 24 different ways total number selected

6. Permutations of n Objects, Not all Distinct Given n objects with n1 (non-distinct) of type 1, n2 (non-distinct) of type 2,…, nr (non-distinct) of type r where n = n1 + n2 + … + nr then number of permutations of these n objects taken n at a time is given by

7. Ex. How many distinguishable arrangements are there of the letters of the word initializing? There are 12 letters n appears 2 times i appears 5 times

8. Combinations of n Objects The number of combinations of n distinct objects taken r at a time is given by Ex. Find C(9, 6). = 84

9. Ex. A boy has 4 beads – red, white, blue, and yellow. How different ways can three of the beads be chosen to trade away? This is a combination since they are chosen without regard to order. 4 different ways total number selected