Among eight nominees for two vacancies on a school board arefour men and four wo

Question

Among eight nominees for two vacancies on a school board arefour men and four women. In how many ways can these vacancies befilled if:                                   a)   anytwo of the nominees is selected                                  b)   any two women are selected                                  c)   one man and one woman are selected Among eight nominees for two vacancies on a school board arefour men and four women. In how many ways can these vacancies befilled if:                                   a)   anytwo of the nominees is selected                                  b)   any two women are selected                                  c)   one man and one woman are selected

Explanation / Answer

There are 8 people ( 4men, 4 women) for 2 vacancies. a) Any 2 nominees are selected, i.e we can choose 2 people outof 8 people, Number of ways to do so = 8C2 = 8!/6!2!= 28 b) Any 2 women are seleced i.e we have to choose 2 women outof 4 Number of ways to do so = 4C2 = 4!/2!2!= 6 c) 1 man and 1 woman selected ,i.e we have to choose 1 man outof 4 and 1 woman out of 4 Number of ways to do so = 4C1 X4C1 = 4 X 4 = 16 c) 1 man and 1 woman selected ,i.e we have to choose 1 man outof 4 and 1 woman out of 4 Number of ways to do so = 4C1 X4C1 = 4 X 4 = 16

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