# Tagged Questions

For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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### Find the maximum number of people who participated in exactly three games?

Gauri Apartment housing society organised annual games, consisting of three games: snooker, badminton and tennis. In all, $510$ people were members in the apartments' society and they were ...
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### Finding the data regarding the four racket games.

In a vijantkhand sports stadium, athletes choose from $4$ different racket games (apart from athletes which is compulsory for all) These are tennis, table tennis, squash and badminton. It is ...
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### all but one sub-strings within a cyclic string

over $GF(q)$ where $q\in\mathbb{N}$, we build a string of size $q^n-1$. now, how can I show that it is always possible to construct that string so it contains all sub-strings of size $n$ exactly once, ...
### Find number of ways to seat $n$ boys and $n$ girls in a row so that every boy has at least one girl sitting beside him.
My attempt: I am getting $2^n(n!)^2$ . First I paired $n$ boys and $n$ girls in $n!$ ways then these pairs can be arranged in $n!$ ways and in each of these pairs boy and girl can arrange themselves ...
### Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
Prove that $$(n!)\cdot(m!)^n|(mn)!$$ I can prove it using Legendre's Formula, but I have to use the lemma that  ...