How many ways are there to split a group of 6 boys into two groups of 3 boys each? (The order of the groups does not matter)

(C) 2008 GMAT Club -

Probability and Combinations#16 * 8

* 10

* 16

* 20

* 24

I think the answer is d, but the OA says:

Because the groups are not ordered, we must use formula \(\frac{C_6^3}{2} = \frac{\frac{6!}{3!3!}}{2} = 10\) . We have to divide \(C_6^3\) by 2 because we need to select one group of 3 boys and the other group will be automatically selected. In other words, the three boys left after selecting of 3 from 6 will constitute the other group of 3. That's why we need to consider only the half of instances of \(C_6^3\) .

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