permutations and combinations

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Reva: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Fri Feb 19, 2010 11:52 am; Thanked: 1 times

permutations and combinations

by Reva » Tue May 25, 2010 8:21 am

1. If there are 7 people in a room, but only 4 chairs available, how many different seating arrangements are possible.

2. If a team of 4 people is to be chosen from 7 people in a room, how many different teams are possible.

How are these 2 statements different and how to identify whether it is a permutation or combination question.

please anybody help me explain this

THANKS.

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Source: Beat The GMAT — Problem Solving | Tue May 25, 2010 8:21 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 am; Thanked: 335 times; Followed by:98 members

by Patrick_GMATFix » Tue May 25, 2010 8:36 am

#1 will have a greater answer because it requires not only how many ways can you pick 4 people from 7 (this is a combination and is the same as #2), but also how many different ways you can have those 4 ppl sit in the 4 chairs (this is a permutation; how many ways 4 ppl can be arranged; 4!)

To solve complex combinatorics break them into discrete steps; find the # of ways to accomplish each step; the product of those ways is the number of ways of doing all the steps.

step I: To get 4people from a group of 7, you do 7!/(4!)(3!). This is the answer to #2.

step II: If you also want these ppl to be arranged (to sit in specific chairs), you could then find how many ways 4 ppl can be arranged (4!)

To do both steps (1) select 4ppl (2) arrange them in chairs. Find the product of both steps. This will be the answer to #1

If you use the OG11 or 12, you can find a listing of combinatorics questions from the OGs in the reference section of the Official Guide Companion.

If you use the Solutions Engine and want to practice official combinatorics questions (written like the GMAT), run drills with topic="combinatorics"

-Best of luck,
Patrick

Last edited by Patrick_GMATFix on Tue May 25, 2010 8:43 am, edited 1 time in total.

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 am; Thanked: 135 times; Followed by:7 members

by selango » Tue May 25, 2010 8:40 am

Combination means number of ways r things can be selected from n things (ie)SELECTION

It can found by nCr

Ex:Selection of people for a team,Selection of set of objects from large set of objects

If 4 people to be chosen from 7 people (ie)selecting 4 people from 7 people ,then 7C4 ways are possible

Permutation means number of ways r things can be SELECTED AND ARRANGED at a time from among n things(ie)SELECTION and ARRANGEMENT

It can be found by nPr

Ex:Putting distinct people/objects in distinct places

If there are 7 people and 4 chairs (ie) selecting 4 out people and arranging in 4 chairs,then 7P4 ways are possible

Hope this clarify