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 one group consists of 7 children and the other group consists of 5 children

Solution

Here we have some important part. We have to select a group of 6 which will be finally forming 2 groups with six children. Bu when we select a six group set the remain is also a six group set.

Ways to select 6 from 12 [= ^12c_6]

But when we select 6 from 12 the rest is also a group of six which is already included in the set we calculated. So to get the correct answers we have get the half of the [^12C_6] .

So ways to select 6 from 12 [= 1/2xx^12C_6 = 462]

So we have 462 ways to select groups of 6 children.