Question

How many committees can be formed by choosing 4 men from an organization of a membership of 15 men?


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Answer 1

The selection of the committee members is an illustration of combination

There are 150150 different ways of selecting the committee

How to determine the total selection

The number of members (n) is:

n = 15

The members on the committee are (r):

r = 4

So, the number of selection is:

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

This gives

$^{15}C_4 = \frac{15!}{(15 - 4)!4!}$

Evaluate the differences

$^{15}C_4 = \frac{15!}{9!4!}$

Expand

$^{15}C_4 = \frac{15* 14 * 13 * 12 * 11 * 10 * 9!}{9!4!}$

This gives

$^{15}C_4 = \frac{15* 14 * 13 * 12 * 11 * 10}{4!}$

$^{15}C_4 = 150150$

Hence, there are 150150 different ways of selecting the committee

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