Question 130

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?

Solution

To select first pair, we need to choose 2 students out of 6, this can be done in $$C^6_2$$ ways

Similarly, for the next 2 pairs = $$C^4_2$$ and $$C^2_2$$ ways

Now, to eliminate repetition, required number of ways = $$\frac{C^6_2\times C^4_2\times C^2_2}{3!}$$

= $$\frac{15\times6\times1}{6}=15$$

=> Ans - (C)

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