SOLUTION: 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?

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?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
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?

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

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