# If I have 5 crayons (red, orange, yellow, green, blue) and I randomly choose 4, what are the chances that I do NOT choose green?

$\frac{1}{5}$

#### Explanation:

We have five crayons, one of which is green. If I choose four crayons at random, what are the odds of not picking the green one?

First, let's find the number of ways I can choose four crayons from the five available. This is a combinations problem (the order we pick the crayons doesn't matter). The general formula for a combination is:

C_(n,k)=(n!)/((k)!(n-k)!) with $n = \text{population", k="picks}$

C_(5,4)=(5!)/((4)!(5-4)!)=5

Of those 5, there's only 1 way to pick crayons that don't have green (red, orange, yellow, blue). So there's only a $\frac{1}{5}$ probability of picking 4 crayons without getting a green.