Question

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?

Answer 1

`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="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 `1/5` probability of picking 4 crayons without getting a green.