A committee of 3 is formed from a panel of 5 men and 3 women. Find the :
(a) number of ways of forming the committee ;
(b) probability that at least one woman is on the committee.
(a) 5 men, 3 women
Number of ways of forming the committee = \(^{8}C_{3}\)
= \(\frac{8!}{(8 - 3)! 3!}\)
= 56 ways.
(b) p(no woman) = \(\frac{^{5}C_{3}}{^{8}C_{3}}\)
= \(\frac{10}{56}\)
\(\therefore\) p( at least one woman) = 1 - p(no woman)
= \(1 - \frac{10}{56}\)
= \(\frac{46}{56}\)
= \(\frac{23}{28}\).
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