binomial distribution

Question

In how many ways can a person select 3 golf shirts for vacation from a selection of 10 golf shirts?

Answer 1

We have three selections with each selection having one less possibility than the previous. This is represented as:

10 x 9 x 8

If order mattered, this would be the answer. However, order does not matter. So A, B, C is the same as B, C, A. To compensate for this, we divide the product by how many selection doesn't matter

10 x 9 x 8/1 x 2 x 3 = 720/6 = 120

A person can select 120 different combintations of golf shirts from 10 golf shirts.

Answer 2

you can use the formula n!/r!(n-r)!

choose 3 out of 10

10!/3!(10-3)!

10!/3!(7!)

(10*9*8*7*6*5*4*3*2*1)/((3*2*1)(7*6*5*4*3*2*1)

simplify

(10*9*8)/(3*2*1)

720/6

120 ways