Q51 / 150 · MHT CET 2023 (10 May Shift 1) · Mathematics
A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if committee consists of at least 2 girls and at most 2 boys, are
- A300
- B320
- Correct answerC321
- D322
Solution
A committee of 5 is to be formed from 8 boys and 5 girls so that it consists of at least 2 girls and at most 2 boys.
Total number of ways
$\begin{aligned}
& =(\text { Five girls })+(4 \text { girls })(1 \text { boy })+(3 \text { girls }) \text { (2 boys }) \\
& ={ }^5 \mathrm{C}_5+{ }^5 \mathrm{C}_4 \times{ }^8 \mathrm{C}_1+{ }^5 \mathrm{C}_3 \times{ }^8 \mathrm{C}_2 \\
& =1+(5 \times 8)+(10 \times 28) \\
& =1+40+280 \\
& =321
\end{aligned}$
Hence, the correct answer is option: 'C'.