# 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, - Mathematics

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?

#### Solution

52 families have at most 2 children, while 35 families have more than 2 children.
The selection of 20 families of which at least 18 families must have 2 children can be made in the ways given below.
(i) 18 families out of 52 and 2 families out of 35
(ii) 19 families out of 52 and 1 family out of 35
(iii) 20 families out of 52
∴ Required ways =${}^{52} C_{18} \times {}^{35} C_2 + {}^{52} C_{19} \times {}^{35} C_1 + {}^{52} C_{20} \times {}^{35} C_0$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 18 | Page 16