Question

In a village, there are 87 famílies, of which 52 famílies have atmost 2 children. in a rural development programme, 20 families are to chosen for assistance, of which
atleast 18 famílies must have atmost 2 children. In how many ways can the choice be made ?​

Answer 1

It is given that out of 87 families, 52 families have at most 2 children so other 35 families are of other type. According to the question, for rural development programme, 20 families are to be chosen for assistance, of which at least 18 families must have atmost 2 children. Thus, the following are the number of possible choices: 52C18 × 35C2 (18 families having atmost 2 children and 2 selected from other type of families) 52C19 × 35C1 (19 families having at most 2 children and 1 selected from other type of families) 52C20 (All selected 20 families having atmost 2 children) Hence, the total number of possible choices is

52C18 × 35C2 + 52C19 × 35C1 + 52C20