Question

How many ways can you select a committee of five members from a group of 10 people?

Answer 1

You can select them 5 by 5 or 2 by 2. so 2 ways.

Answer 2

There are 10 ways to pick the first committee member, then there are only 9 choices for the second member, for the third member there are 8 choices, and so on. This gives
\[10*9*8*7*6\]
But that is not the right answer, since this is a specific ordering of the members, and the question only asked for the number of ways that was possible. By a similar argument to the one above, there are
\[5*4*3*2*1\]
ways of ordering 5 things. So if we divide the first by the second we get the answer to the question:
\[\frac{10*9*8*7*6}{5*4*3*2*1}=252\]