A class consist of 40 girls & 60 boys. In how many ways a president , vice president , treasurer , secretary be chosen. If the treasurer must be a girl & secretary must be a boy and a student cannot hold more than one position.

The treasurer can be selected from the 40 girls in ^{40}C_{1} ways, i.e., in 40 ways.

The secretary can be selected from the 60 boys in ^{60}C_{1} ways, i.e., 60 ways.

We now have 100 – 2 = 98 students left for two positions – president and vice president.

The two can be selected in ^{98}C_{2} ways and can be arranged in 2 ways i.e. the first person selected can be either the president or the vice president.

Hence this can be done 2×^{98}C_{2} ways.

(OR we can say that the president can be selected in ^{98}C_{1} (i.e. 98 ways) and vice president can be selected in ^{(98 – 1)}C_{1} ways= 97 ways).

Total ways of selection = 40 × 60 × 98 × 97 = 22814400.

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