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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P & C
This topic has expert replies
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
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
