Question

I was wondering - how many different possible ways can you make groups of 3 if you have 15 people in total? It's important to note that two these people absolutely cannot be in the same group together. Thanks a bunch!

Answer 1

Total ways to make a group of 3 from 15 people without any condition =

Now we need to remove those groups in which 'two of those people are in same group'. If we assume that both of them are in a group then the 3rd person can come by 13 ways. As we have 3 places, 2 places are already filled so only one place left to fill and out of 15 we already have 2 persons in the group so remaining are 13 people which can come into group.

So, total number of groups such that two of these people absolutely cannot be in the same group together = 455 - 13 = 442.

Hence, 442 is the answer.

Please comment if any doubt. Thank you.