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# DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)

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Joined: 02 Sep 2009
Posts: 52431
DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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Updated on: 02 Jan 2018, 01:40

DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)

 ! This post is a part of the Special Questions Directory focusing on Quant topics traditionally neglected and not covered by conventional sources but still tested on the GMAT. Many of these are above average difficulty questions

Combinatorics questions which deal with dividing/distributing entities into groups.

THEORY

Unfair Distributions in Combinatorics - Part I
Unfair Distributions in Combinatorics - Part II

FORMULAE

1. The number of ways in which $$mn$$ different items can be divided equally into $$m$$ groups, each containing $$n$$ objects and the order of the groups is important is $$\frac{(mn)!}{(n!)^m}$$

2. The number of ways in which $$mn$$ different items can be divided equally into $$m$$ groups, each containing $$n$$ objects and the order of the groups is NOT important is $$\frac{(mn)!}{(n!)^m*m!}$$.

3. The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0, 1, 2 or more items $$n+r-1Cr-1$$

4. The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is $$n-1Cr-1$$

QUESTIONS

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HARD (FOR PRACTICE): https://gmatclub.com/forum/5-rings-on-4 ... 86111.html
_________________

Originally posted by Bunuel on 02 Jan 2018, 00:53.
Last edited by Bunuel on 02 Jan 2018, 01:40, edited 1 time in total.
Edited.
Math Expert
Joined: 02 Sep 2009
Posts: 52431
DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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02 Jan 2018, 00:53
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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29 Jan 2018, 07:23
Re: DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION) &nbs [#permalink] 29 Jan 2018, 07:23
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# DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)

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