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?
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
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