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?

1 Answer



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"#


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.