Suppose I have an urn containing balls D of k different colors. Let D_i be the subset of D of all the balls having the ith colour. The probability of randomly selecting (without replacement) y_1 balls from D_1, y_2 balls from D_2, . . . , y_k balls from D_k is, of course, given by the multivariate hypergeometric distribution. What I am interested in is the total number of ways of selecting n balls from D.
For example, if D = [2  1  2] (i.e., k = 3), and n = 3, then the possible ways of selecting n balls from D are
[2  1  0]
[2  0  1]
[1  1  1]
[1  0  2]
[0  1  2]
In the above example, the number of ways of selecting 3 balls from D is 5, but is there a general mathematical expression for the total number of ways of selecting n balls from D?
Total number of ways of selecting n balls from an urn with k colours
Re: Total number of ways of selecting n balls from an urn with k colours
[Solved]
The answer is given on page 138 of Charalambides, C. A. (2002) Enumerative Combinatorics, Chapman & Hall/CRC.
The answer is given on page 138 of Charalambides, C. A. (2002) Enumerative Combinatorics, Chapman & Hall/CRC.

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Re: Total number of ways of selecting n balls from an urn with k colours
It would be great if you can share the solution here...
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