(Q). A work can be compelted by 5 men or 7 women in 4 days. In how many ways labour force can be selected if work has to be finished in 4 days & available labour force is 12 men & 10 women? If labour force has only men or only women.
Solution:-
case(i): when work is completed by men then number of ways of selecting labour force i.e. 5 men out of 12 men is
¹²C₅ = 792
case(ii): when work is completed by women then number of ways of selecting labour force i.e. 7 women out of 10 women is
¹⁰C₇ = 120
Hence required number of ways = 792 + 120 = 912 ways Answer