WAEC - Further Mathematics (2006 - No. 17)
A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?
15
40
70
175
설명
From the five(5) men viable for the position of the chairman, one of them must be selected.
This implies; 4 men and 3 women are open for committee membership.
7 C\(_3\) = \(\frac{7!}{3!(7 - 3)!}\) =
\(\frac{7⋅6⋅5⋅4⋅3⋅2⋅1}{3.2.1 \times 4.3.2.1}\)
= 35 \(\times\) 5 = 175