# Urn Problem

1. Sep 16, 2010

### MartinWDK

Dear all,

We are trying to compute the number of ways for a computer to execute concurrent processes.
It appears that this problem is equivalent to asking the following:

Assume that an urn is filled with different quantities of differently colored balls. There are k different colors, and the number of balls of a given color is denoted nk.
Balls are drawn from the urn it is empty, and the color of the drawn ball is noted.

The question is: how many different color sequences can be constructed in this way?

Thank you,

Martin

2. Sep 16, 2010

### csopi

Let N=n1+n2+...+nk

$$\frac {N!}{n_1!\dots n_k!}$$
because there would be N! possibilities if the colours were pairwise different, but they are not, so we counted each possibility a lot of times. One can permutate the balls from the jth colour n_j! ways but when doing so we don't see any difference in the colour-sequence, so we have to divide N! by n_1!...n_k!

3. Sep 16, 2010

### MartinWDK

Hi csopi,

Thank you for a quick reply and for a clear and coherent explanation!

The formula matches our calculations, so I think we have our answer :)

Best regards,

Martin