Combinatorics without repetition with order, limits and duplicates

Asked Jun 28 '21 at 05:32

Active Jun 28 '21 at 09:44

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I'm new here, and I came across a problem that probably has already been answered before, but I couldn't find it.

I have $n$ types of balls with different quantities, with $a_1$ balls of type 1, $a_2$ balls of type 2, and so on. How many different ways are there to arrange $K$ balls in a row, where $K < n$?

edited Jun 28 '21 at 09:44

N. F. Taussig

79,074

asked Jun 28 '21 at 05:32

eilon toledano

Is $k=\Sigma{a_i}$ ? – true blue anil Jun 28 '21 at 06:52
it not the case, I update the question – eilon toledano Jun 28 '21 at 09:32
Welcome to MathSE. This tutorial explains how to typeset mathematics on this site. – N. F. Taussig Jun 28 '21 at 09:45
See also the linked questions at that answer for more information. – Mike Earnest Jun 28 '21 at 16:50

Combinatorics without repetition with order, limits and duplicates

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