How many ways are there of choosing 5 colors, without replacement, from 16 distinct colors, if the order of the choices is relevant

Whenever you have a collection of N items from which you are going to choose K of them without replacement, the number of possible combinations is either:

A) If order matters: P(N,K) = N x (N-1) x (N-2) *... *(N-K+1). This is called the "permutation" of N items taken K at a time. The reason is that you can pick any one of the N items for the first choice, then any of the (N-1) remaining items for the second, etc.

B) If order doesn't matter - in other words picking items A, B, and C is considered the same as picking items A, C, and B - then the answer is: C(N,K) = P(N,K)/K! This is the "combination" of N items taken K at a time. The reason is that starting with the answer for (A) you must divide by K! Because for each set there are K! That are repeats in different order.

Now can you apply this to your problem? Post back with what you get.