1. 3.2 Combinations

2. Combinations Counting where order doesn’t matter.
Combination Formula: nCr = n!/r!(n-r)!
Example: We have a deck of cards and we want 5 cards. They can be any cards. There are 52 cards to a deck.
52C5 52!/5!(52-5)! = 2,598,960

3. K selections are made from n items, without regard to order and repeats are allowed.
The number of ways these selections can be made is n+K-1CK

4. Example Number of CD’s to choose from = 10
K = 3 (the number of CD’s that can be ordered)
10+3-1C3 = 12C3
= 12!/3!(12-3)!
= 12!/3!9!
= /(6)(362880)
= /
= 220

5. When order doesn’t matter, we count the number of subsets or combinations. When order matters, we count the number of sequences or permutations.
How many different 7 person committees can be formed, each containing three women from an available set of 20 women, and four men from an available set of 30 men.

6. Task 1: Choose 3 women from the set of 20 women
Task 2: Choose 4 men from the set of 30 men
30C !/4!(30-4)! = 30!/4!26! = 27,405
(1140)(27405) = 31,241,700 different committees