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

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DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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New post Updated on: 02 Jan 2018, 02:40

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

https://gmatclub.com/forum/in-how-many- ... 87128.html
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https://gmatclub.com/forum/in-how-many- ... 98697.html
https://gmatclub.com/forum/how-many-pos ... 85291.html
https://gmatclub.com/forum/how-many-way ... 37198.html
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https://gmatclub.com/forum/mrs-smith-ha ... 98225.html
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https://gmatclub.com/forum/four-boys-pi ... 98701.html
https://gmatclub.com/forum/how-many-way ... 61598.html
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https://gmatclub.com/forum/in-how-many- ... 34223.html
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https://gmatclub.com/forum/mel-and-nora ... 34163.html
https://gmatclub.com/forum/in-how-many- ... 51692.html
https://gmatclub.com/forum/in-how-many- ... 43863.html
https://gmatclub.com/forum/in-how-many- ... 34222.html
https://gmatclub.com/forum/in-how-many- ... 47854.html
https://gmatclub.com/forum/larry-michae ... 82046.html
https://gmatclub.com/forum/if-josh-doug ... 24273.html

HARD (FOR PRACTICE): https://gmatclub.com/forum/5-rings-on-4 ... 86111.html
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Originally posted by Bunuel on 02 Jan 2018, 01:53.
Last edited by Bunuel on 02 Jan 2018, 02:40, edited 1 time in total.
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DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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New post 02 Jan 2018, 01:53

21. Combinatorics/Counting Methods



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hope it helps.
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Re: DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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New post 29 Jan 2018, 08:23
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Re: DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)  [#permalink]

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New post 26 Aug 2019, 11:13
Hello from the GMAT Club BumpBot!

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Re: DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION)   [#permalink] 26 Aug 2019, 11:13
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