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MGMAT Combinatorics Probem Sets

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by theachiever » Tue Oct 30, 2012 10:48 pm
Problem Set

A delegation from City A goes to City B to discuss a limited X-Y Combination Partnership.If the Mayor of City B chooses 3 members of the 7 person delegation to meet with Y ,how many different 3-person combinations can he choose?
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by pemdas » Tue Oct 30, 2012 11:30 pm
theachiever wrote:Problem Set

A delegation from City A goes to City B to discuss a limited X-Y Combination Partnership.If the Mayor of City B chooses 3 members of the 7 person delegation to meet with Y ,how many different 3-person combinations can he choose?
7C3=7!/(4!*3!)=35 ways
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by theachiever » Tue Oct 30, 2012 11:35 pm
2.A Spy of a certain country X is trying to escape from his prison cell.The lock requires him to enter one number, from 1-9,and then push a pair of colored buttons simultaneously.He can make one attempt every 3 seconds.If there are 6 colored buttons,what is the longest possible time it could take the spy to escape from prison cell?
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by pemdas » Wed Oct 31, 2012 2:31 am
theachiever wrote:2.A Spy of a certain country X is trying to escape from his prison cell.The lock requires him to enter one number, from 1-9,and then push a pair of colored buttons simultaneously.He can make one attempt every 3 seconds.If there are 6 colored buttons,what is the longest possible time it could take the spy to escape from prison cell?
all options include 9 numbers entered combined with a pair of two buttons pressed simultaneously out of six (order doesn't matter) 6C2 Or 9*6C2=135 attempts in total. Considering for each attempt a Spy spends 3 seconds makes the longest time 135*3/60=135/20=6 3/4 Or 6 minutes and 45 seconds.
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by Brent@GMATPrepNow » Wed Oct 31, 2012 6:33 am
Please post only one question per thread. Otherwise things can get complicated if there are discussions on multiple questions.

Cheers,
Brent

PS: If anyone is interested, we have a free video on calculating combinations (like 7C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
Brent Hanneson - Creator of GMATPrepNow.com
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