Question 978502
In how many ways can a class of 20 pupils be split into two groups of 8 and 12,If there is two twins who can't be separated?
<pre>
We only need to choose the group of 8, for the ones not chosen will make up the
group of 12.

Case 1: The set of twins are in the group of 8.

We choose the other 6 in that group from the 18 non-twins in 18C6 ways. 

Case 2: The set of twins are NOT in the group of 8.

We choose all 8 from the 18 non-twins in 18C8 ways.

Answer: 18C6  + 18C8 = 18564 + 43758 = 62322 ways.

Edwin</pre>