# Math Help - Combinations type question...

1. ## Combinations type question...

Ok, stuck on this problem..

Suppose you have 6 letters: A, B, C, D, E , F

And you are allowed to pick 3 but with the following rules:

1. ABC is the same as ACB, BCA etc so they are not counted as unique
2. repetitions are allowed so AAB is allowed or CCC

How many would there be in total...after playing around i think there are 56, but i would like a general approach and a generalisation... So n letters and you are allowed to pick q with the rules above.

Many thanks

2. ## Re: Combinations type question...

You can obtain a solution using formula for combinations with repetition :

$N=\frac{(n+k-1)!}{k! \cdot (n-1)!}$

In this particular case :

$N=\frac{(6+3-1)!}{3! \cdot (6-1)!}=56$

3. ## Re: Combinations type question...

Wow.. can you explain where you got this result from please? Or how it is derived?

4. ## Re: Combinations type question...

Originally Posted by rodders
can you explain where you got this result from please? Or how it is derived?
These are known as multi-sets,