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.
Explanation
(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}).