Question

Two teachers from each stream are to be included?

• A. 210
• B. 180
• C. 145
• D. 96
• E. None of these

Answer 1

The correct option is B 180

When two teachers from each stream are to be included, then number of ways
${=}^4{C}_2{\times }^5{C}_2{\times }^3{C}_2=\frac{4!}{(4-2)!\times 2!}\times \frac{5!}{(5-2)!\times 2!}\times \frac{3!}{(3-2)!\times 2!}=\frac{4\times 3\times 2!}{2!\times 2\times 1}\times \frac{5\times 4\times 3!}{3!\times 2\times 1}\times \frac{2!\times 3}{1\times 2!}$
$=2\times 3\times 5\times 2\times 3=180$