Question

17. A group consists of 7 men and some women. The probability of
selecting 2 women from them is 1s. Find the number of women in
the group
[Ans. : 3]
​

Answer 1

Answer:

There are 3 women in the group.

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Step-by-step explanation:

Let w be the number of women.

The number of people is then w+7.

P(2 people chosen are women) = 1/15

=> ( # ways to choose 2 women ) / ( # ways to choose 2 people ) = 1 / 15

=> 15 × ( # ways to choose 2 women ) = # ways to choose 2 people

=> 15 w ( w - 1 ) / 2 = ( w + 7 ) ( w + 6 ) / 2

=> 15w² - 15w = w² + 13w + 42

=> 14w² - 28w - 42 = 0

=> w² - 2w - 3 = 0

=> ( w - 3 ) ( w + 1 ) = 0

=> w = 3 ( since the number of women is non-negative).

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