# From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains at least 3 boys. - Mathematics and Statistics

Sum

From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains at least 3 boys.

#### Solution

The group consists of 8 boys and 5 girls
i.e., 8 + 5 = 13 persons.
A committee of 5 is to be formed from this group.
∴ 5 persons from 13 persons can be selected in 13C5 ways
∴ n(S) = 13C5
Let B be the event that the committee contains at least 3 boys (i.e., 3 boys and 2 girls or 4 boys and 1 girl or 5 boys and no girl)

∴ n(B) = 8C3 × 5C2 + 8C4 × 5C1 + 8C5 × 5C0

∴ P(B) = ("n"("B"))/("n"("S")

= (""^8"C"_3  xx ""^5"C"_2 + ""^8"C"_4 xx ""^5"C"_1 + ""^8"C"_5xx""^5"C"_0)/(""^13"C"_5)

Concept: Elementary Properties of Probability
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