NDA 2023 Maths · Mathematics · Permutations and Combinations · medium

A team of 4 is to be selected from 6 boys and 3 girls so that it contains exactly 2 girls.

Single correct option

A team of 4 is to be selected from 6 boys and 3 girls so that it contains exactly 2 girls. The number of ways is

Show answer and solution

Answer: (B) $45$

Choose the 2 girls from 3 in

\binom32=3

ways and the other 2 members from the 6 boys in

\binom62=15

ways. Multiply (independent choices):

3\times15=45

. Multiplying by an extra factor of

2

for the order of selection double counts and gives

90

, and

\binom62=15

alone ignores the girls.

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake