# Combinations on Multisets.

I was looking at this question Probability of selecting four letters from ENCYCLOPAEDIA and my mind started to wander.

What would you have to do to handle the double B in question 2 compared to question 1.

1. You have a bag of 5 letters. A,A,B,C,D. If you choose 3 How many combinations are there with exactly one A.

2. You have a bag of 5 letters. A,A,B,B,C. If you choose 3 How many combinations are there with exactly one A

• @Rafael Thank you. – Tolure Feb 21 at 16:35
• The answer to question $1$ is $3$ and the answer to question $2$ is $2$. I'm not sure what you're driving at. – saulspatz Feb 21 at 16:41
• Looking for how to approach the question (work involved) not just the answer which I could do by writing them all out. – Tolure Feb 21 at 16:48

In first case, in your combination there should be one $$A$$ and an arbitrary combination of two letters from the three different non-$$A$$s. You can select them in $$3$$ different ways. So the answer is $$3$$.
In the second case you also select one $$A$$, but then you have only two choices: to select a $$B$$ and a $$C$$, or to select two $$B$$-s. So the answer is $$2$$ now.