How many different 3 people committees can be formed from a group of 25 people?

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Answer 1 · 2016-01-17T00:58:06

Use the combination formula, #(n!) / {r!(n - r)!#

This problem is a combination problem since order doesn't matter.

n = the total number of elements, in this case 25

r = the number being picked, in this case 3

Plug n and r into the formula:

#(25!) / {3!(25 - 3)!#

= #(25!) / {3!(22)!#

= 2300

So, there are 2300 different committees that can be formed.

Here is a problem for you practice:

14 people apply for a job. Only 2 positions are available. Find the number of different combinations of employees possible.