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Question
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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Solution
It is given that out of 87 families
52 families have at most 2 children
So other 35 families are of other type.
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 × 35C2 (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 × 35C2 + 35C1 + 52C20
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