Q35Long answer
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: C18 × 35C2 (18 families having atmost 2 children and 2 selected from other type of families) C19 × 35C1 (19 families having at most 2 children and 1 selected from other type of families) C 20 (All selected 20 families having atmost 2 children) Hence, the total number of possible choices is C18 × 35C2 + 52C19 × 35C1 + 52C20