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?

Explanation

There are total `87` families out of which `52` families have at most two children.

It means there are `35` families that have more than two children.

Now, we have to choose `20` families of which at least `18` families have at most two children.

So, there are three cases:

a) When `18` families are selected from `52` families that have at most two children and `2` families from rest of `35` families.

Total number of ways in this case ` = C(52,18)*C(35,2)`

b)When `19` families are selected from `52` families that have at most two children and `1` families from rest of `35` families.

Total number of ways in this case ` = C(52,19)*C(35,1)`

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