Question

How many ways can a committee of 4 people be chosen from a group of 8 people if the members are selected in no particular order?

Answer 1

70

Explanation:

There are 8 choices for the first member, 7 for the second, 6 for the third, and 5 choices for the fourth member (because once you pick someone as a member, they cannot be picked again)

So you have:

8*7*6*5 = 1680

However, we realize that in this particular problem, order DOES NOT matter. (for example, ABCD is the same as DCBA.)

So we divide 1680 by 4! (4*3*2*1) to end up with 70.

You do this because because there are 4! ways to arrange 4 people in a line, and since order doesn't matter, only one of those arrangements counts.