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

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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 at most 2 children. Thus, the following Are the number of possible choices: 

52C8 × 35C2 (18 families having at most 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) 

Hence, the total number of possible choices is 

52C18 × 35C2 + 52C19 × 35C1 + 52C20

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