Question

There are 9 different colors of paint to choose from. Out of the 9 colors, how many ways can 4 different colors be chosen?

Answer 1

`9xx8xx7xx6 = 3,024`

Explanation:

Think about choosing 4 colours, one at a time.

There are 9 choices for the first colour. The colours have to be different, so that one cannot be chosen again, 8 colours are left.

There are 8 choices for the second colour, and in the smae way, 7 choices for the third colour and 6 choices for the fourth colour.

The total number of possibilities is:

`9xx8xx7xx6 = 3,024`

This can also be written as `(9!)/((9-4)!) = (9!)/(5!)`

Note why this works:

`(9xx8xx7xx6xxcancel(5xx4xx3xx2xx1))/(cancel(5xx4xx3xx2xx1))`