10.3 – Using Permutations and CombinationsPermutation: 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 CombinationsFactorial Formula for Permutations

!.

( )!n rn

Pn r

Factorial Formula for Combinations

!.

! !( )!n r

n rP n

Cr r n r

10.3 – Using Permutations and CombinationsEvaluate each problem.

c) 6P6a) 5P3b) 5C3 d) 6C6

54360 10 720 1

10.3 – Using Permutations and CombinationsHow 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.

26P2 10P3

2625650 1098720650720468,000

10.3 – Using Permutations and CombinationsA 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.

52C5

2,598,960 5-card hands

10.3 – Using Permutations and CombinationsFind 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}.

9C3

84 Different subsets

9P3

987504 arrangements

10.3 – Using Permutations and CombinationsGuidelines on Which Method to Use