Combinations

${}_n$C${}_r$ or C(n,r) or (n/r). A selection from a group of items without regard to order

Combinations Formula

${}_n{C}_r=\frac{{}_n{P}_r}{r!}$ = $\frac{n!}{(n-r)!(r!)}$

Concepts

• Combination Subset Formula
• Combinations with Repetition
• Divisors with Combinations
• Hockey Stick Identity
• Problem Solving with Combinations

Examples

Example 1

in how many ways can: A, B, C, D and E, create a comittee? 5 People, 3 boxes The order doesn’t matter. they are the same comittee. To find this, you find the permutations, then divide by the permutations the boxes can have.

1. Permutations: ${}_5$P${}_3$ = 60
2. Duplicate boxes = 3! = 6. Example:
3. 60/6 = 10

Example 2

How many different sampler dishes can you have with 3 different flavors could you get in an ice cream shop with 31 different flavors? doesn’t matter what order the flavors are in.

n = 31
r = 3
31!/(28!)(3!)
= 4495