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 40C1 ways, i.e., in 40 ways.
The secretary can be selected from the 60 boys in 60C1 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 98C2 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 2×98C2 ways.
(OR we can say that the president can be selected in 98C1 (i.e. 98 ways) and vice president can be selected in (98 – 1)C1 ways= 97 ways).
Total ways of selection = 40 × 60 × 98 × 97 = 22814400.