Chapter 1

Section 11-3I CAN: Use Permutations and

Combinations

Guidelines on Which Method to Use

Permutations CombinationsOrder 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

1-3-3

Factorial Formula for Permutations

Arrangements are called permutations The number of permuations of n things taken r at a time is denoted as: ! .

( )!n rnP

n r

ORDER MATTERS

n = _________________r = _________________

n must be greater than r

*Can’t have more #s in a subset than the total # of items!

Example: Permutations

Evaluate each permutation.

a)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:

! .! !( )!

n rn r

P nCr r n r

*ORDER DOES NOT MATTER*

The # of combinations of n things taken r at a time

Example: Combinations

Evaluate each combination.

a)5C3 b) 7C2

11-3-9

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