P & C

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

by rahul.s » Tue Jan 12, 2010 7:15 am

What is the number of ways in which 5 students can be made to stand in a row for a photograph such that the shortest and tallest are never together?

A) 84
B) 120
C) 96
D) 72
E) 60

OA: D
Source: PBT

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Source: Beat The GMAT — Problem Solving | Tue Jan 12, 2010 7:15 am

aakar: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Sep 02, 2009 6:06 am; Thanked: 1 times

by aakar » Tue Jan 12, 2010 8:25 am

I could have approached this the wrong way, but this is the way I approached it:

Total number of ways w/out restriction: 5! = 120
Total number of ways w/ restriction (Take the shortest and tallest as 1 unit) = 4! = 24

However remember that you could have shortest standing first and tallest second or tallest first and shortest second, as a result total number of ways w/ restriction needs to be multiplied by 2 = 48

Thus 120 - 48 = 72

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