A committee of 4 Students is to be chosen from 5 boys and 3 girls Find the probability that the comm...........

Quantitative Aptitude (CDS) Probability

A committee of 4 Students is to be chosen from 5 boys and 3 girls. Find the probability that the committee contains exactly 3 boys?

15/28

1/15

1/28

1/2

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Explanation:

4 students can be selected from 8 in 8C5 ways.
Therefore , n(T) = 8C5 = 8!/3!×5!
= 56
Let E be the event that the committed includes exactly 3 boys and 1 girl.
The 3 boys can be selected in 5C3 ways and 1 girl can be selected in 3C1 ways.
Thus , n(E)= 5C3 × 3C1
= 30
Therefore , P(E)= n(E)/n(T)
= 30/56 = 15/28