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Re: puzzle with string permutations [photo]

From: Emanuel Berg
Subject: Re: puzzle with string permutations [photo]
Date: Wed, 08 Jun 2022 00:04:16 +0200
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux)

Yuri Khan wrote:

> This extension of the concept of sets is called a multiset
> or a bag. For each element, we also have a multiplicity.
> Let’s write it as {o:2, g:1, d:1}.

OK, cool!

> n_perm = (n_1 + ... + n_k)! / (n_1)! ... (n_k)!

Right, that's tedious to do programming of tho (but possible
of course) because of the expanding summation and
product ...

> This problem was part of my exam in maths when I was
> applying at Novosibirsk State University, Mechanics & Maths
> Department, in 1997.


> You might also notice the formula is similar to that of
> a binomial coefficient: C_{n,k} = n! / k! (n-k)!. That's
> no coincidence.

That OTOH is easy to implement, but what is n and k exactly? Can you
use that here?

(defun binom (n k)
  (/ (cl-faculty n)
     (* (cl-faculty k)
        (cl-faculty (- n k)) )))

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