# [SOLVED] How many combinations are there in cases where there are identical objects?

• Apr 3rd 2010, 03:38 PM
hasbren
[SOLVED] How many combinations are there in cases where there are identical objects?
Here's my problem: I have forty marbles. 20 of them are black, 20 are white. If I pull them all out and record them, (for example, w,b,w,w,w,b,w,....) how many different combinations are possible?

For cases without identical objects the answer would be (40!), but when they are separated into two identical objects, I don't know the answer.

• Apr 3rd 2010, 03:45 PM
hasbren
Nevermind- I think I found my answer here:

Permutations and Combinations
• Apr 3rd 2010, 03:50 PM
Plato
Quote:

Originally Posted by hasbren
Here's my problem: I have forty marbles. 20 of them are black, 20 are white. If I pull them all out and record them, (for example, w,b,w,w,w,b,w,....) how many different combinations are possible?

This is an incomplete question! You did not tell us how many are taken.
Nor did you say if the marble is replaced each time.

Let’s say that all forty marbles are drawn one at a time without replacement.
Recording the color of each then there are $\frac{40!}{(20!)^2}$ possible patterns.
• Apr 3rd 2010, 03:54 PM
hasbren
Yes, that was my question, and that is the correct answer-- sorry for not being more clear!