In a small village, there are 87 families, of which 52 families have a

1.	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?
Answer» 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 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 × ³⁵C₁(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 × ³⁵C₁ + ⁵²C₂₀

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?

Answer»

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 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 × ³⁵C₁(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 × ³⁵C₁ + ⁵²C₂₀

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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