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

1 Answer
Nov 23, 2016

Answer:

#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))#