[DiceyPlay]

If you were asked how many ways can you choose 2 items out of a collection of 5 distinct items a short hand way of asking this is to write C(5,2).

The formula to evaluate C(5,2) is 5!/(2! * (5-2)!) and ! is a factorial which is evaluated as follows:

To evaluate n! it is equal to n * (n-1) * (n-2) * (n-3) * ... * 3 * 2 * 1

so C(5,2) = 5!/(2! * (5-2)!) = 5 * 4 * 3! / (2 * 3!) = 5 * 4 / 2 = 10.

Therefore there are 10 ways to choose 2 items from a collection of 5 distinct items.

Notice the order in which you choose the items from the collection does not make a difference. This is a combination. If it did make a difference, it would be a permutation. The formula to evaluate a permutation is P(n,r) = n! / (n-r)!

Hope that makes sense.