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

The Correct Option is C

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