A group of ten women and ten men are in a room. a committee of four is chosen at random. find the probability that the committee consists only of women?

Question

Mathematics

Redbull

12 May, 22:57

A group of ten women and ten men are in a room. a committee of four is chosen at random. find the probability that the committee consists only of women?

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Answers (1)

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Bentley Stokes · Answer 1

First, we determine the sample space of choosing four members of the committee from 20 persons (both men and women). That is,

20C4 = 4845

Then, we determine the combination of choosing these 4 members only from the group of women. That is,

10C4 = 210

The probability is calculated by dividing the second answer by the first answer which will give us an answer of 14/323.