Question

A committee of $5$ is to be formed from $6$ boys and $5$ girls. The number of ways that the committee can be formed, so that the committee contains at least two boys and two girl is

• A. 248
• B. 350
• C. 720
• D. 1025

Answer 1

Answer: (B)

350

The committee of $5$ has to be formed in which at least two boys and two girls is must and we have total $6$ boys and $5$ girls.

So our choices are to select two boys and three girls or three boys and two girls out of six boys and five girls
Hence, required number of ways ${=}^6{C}_2{\times }^5{C}_3{+}^6{C}_3{\times }^5{C}_2$

$=15\times 10+20\times 10$

$=350$