A group consists of 6 boys and 5 girls. The number of committees of 4 persons that can be formed, if the…
A group consists of 6 boys and 5 girls. The number of committees of 4 persons that can be formed, if the committee consists of at least 2 girls and at most 2 boys, is:
200
215
220
225
Solution
To form a committee of 4 persons with at least 2 girls and at most 2 boys from a group of 6 boys and 5 girls, we consider the following combinations:
1. $\mathbf{2}$ girls and 2 boys:
$\binom{5}{2} \times\binom{ 6}{2}=10 \times 15=150$
2. 3 girls and 1 boy:
$\binom{5}{3} \times\binom{ 6}{1}=10 \times 6=60$
3. $\mathbf{4}$ girls and 0 boys:
$\binom{5}{4} \times\binom{ 6}{0}=5 \times 1=5$ Total number of ways:
$150+60+5=215$ Thus, the correct answer is option (2) 215.