Question

Suppose we want to choose 7 colors, without replacement, from 9 distinct colors
If the order of the choices does not matter, how many ways can this be done?

Answer 1

The number of ways to choose the colors is 36

How to determine the number of ways?

The given parameters are:

Colors = 9

Colors to choose = 7

Since order does not matter, then it is combination

This is calculated using:

$^nC_r = \frac{n!}{(n - r)!r!}$

This gives

$^nC_r = \frac{9!}{7!2!}$

Evaluate

$^nC_r = 36$

Hence, the number of ways is 36

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