Question

In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made ?

Answer 1

52 families have at most 2 children, while 35 families have 2 children.

The selection of 20 families of which at least 18 families must have at most 2 children can be made as under

(i) 18 families out of 52 and 2 families out of 35

(ii) 19 families out of 52 and 1 family out of 35

(iii) 20 families out of 52

Therefore the number of ways are

${}^{52}{C}_{18}{\times }^{35}{C}_2{+}^{52}{C}_{19}{\times }^{35}{C}_1{+}^{52}{C}_{20}{\times }^{35}{C}_0$