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

Nov 23, 2016

$9 \times 8 \times 7 \times 6 = 3 , 024$

#### 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:

$9 \times 8 \times 7 \times 6 = 3 , 024$

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

Note why this works:

$\frac{9 \times 8 \times 7 \times 6 \times \cancel{5 \times 4 \times 3 \times 2 \times 1}}{\cancel{5 \times 4 \times 3 \times 2 \times 1}}$