It is required to divide 12 children of different heights in

It is required to divide 12 children of different heights into two groups.
Find the number of ways in which this can be done .

If each group consists of 6 children and if the tallest and the shortest must be in the same group.

Solution

We have to select groups of 6 students but the condition is that we need tallest and shortest in the same group. So two positions of one group is already filled. So what we have to do is to fill he rest four from the possible ten left.

Ways to select 4 from 10 `= ^10C_4 = 210`

So the ways this can be done is 210.