Question

In how many ways can 4 singers be selected from 8 who came to an audition?

Answer 1

The first selection can be any one of the 8. 
               For each one ...
The second selection can be any one of the remaining 7. 
               For each one ...
The third selection can be any one of the remaining 6. 
               For each one ...
The fourth selection can be any one of the remaining 5.

Total number of ways to select four = (8 x 7 x 6 x 5) = 1,680 ways

BUT ... There are not 1,680 different groups of 4 .

Each group of 4 can be selected in (4 x 3 x 2) = 24 different ways.

So, although there are 1,680 different ways to select 4 singers,
there are only
                           (1,680 / 24) = 70 different groups of 4
                                                     that you can end up with.