Question

In a class-room, there are 6 students. We need to divide them into 3 pairs for the purpose of assigning homework. In how many ways can we make such pairs?

• A. 5
• B. 6
• C. 15
• D. 24

Answer 1

Answer: (C)

15

Answer 2

To select first pair, we need to choose 2 students out of 6, this can be done in $C\frac{6}{2}$ways
Similarly, for the next 2 pairs =$C\frac{4}{2}$ and $C\frac{2}{2}$ ways
Now, to eliminate repetition, required number of ways =$\frac{C\frac{6}{2}C\frac{4}{2}C\frac{2}{2}}{3!}$
$\frac{15\times6\times1}{6}=15$
The correct answer is (C) : 15