nForum - Discussion Feed (multinomial coefficient) 2022-01-29T00:18:16-05:00 https://nforum.ncatlab.org/ Lussumo Vanilla & Feed Publisher Todd_Trimble comments on "multinomial coefficient" (66948) https://nforum.ncatlab.org/discussion/8243/?Focus=66948#Comment_66948 2018-01-19T12:44:26-05:00 2022-01-29T00:18:16-05:00 Todd_Trimble https://nforum.ncatlab.org/account/24/ Added the justification via counting the number of permutations.

Added the justification via counting the number of permutations.

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zskoda comments on "multinomial coefficient" (66947) https://nforum.ncatlab.org/discussion/8243/?Focus=66947#Comment_66947 2018-01-19T11:17:20-05:00 2022-01-29T00:18:16-05:00 zskoda https://nforum.ncatlab.org/account/10/ I added In combinatorics, the definition usually extends to k=0k = 0 by setting 0!=10! = 1. The same for binomial/multinomial coefficients, the numbers k ik_i and nn can be zero as it is in ...

In combinatorics, the definition usually extends to $k = 0$ by setting $0! = 1$.
The same for binomial/multinomial coefficients, the numbers $k_i$ and $n$ can be zero as it is in Pascal triangle, then one uses $0! = 1$. (In fact, there are also the standard conventions when some of the numbers are out of bound when the multinomial coefficients are, in combinatorics, taken to be zero.) Our entry binomial theorem anyway uses the summation where the lower index is allowed to be zero as it should be.