vikasp99 wrote:
John and four friends go to a Lakers game. In how many ways can they be seated in five consecutive seats, if John has to sit between any two of his friends?
(A) 144
(B) 120
(C) 96
(D) 72
(E) 48
Hey,
PFB the solution.
Let us first make
5 spaces representing the 5 seats.
___ ___ ___ ___ ___
As per the given condition,
John has to sit between any two of his friends, that mean John
cannot sit at the first and the last seat.
Therefore, the total number of ways in which John can sit is 3.
__ _J_ __ __ __ OR __ __ _J_ __ __ OR __ __ __ _J_ __
Now we are left with 4 friends who can occupy any of the four seats without any restriction in \(^4P_4\) ways \(= 4! = 24\)
Thus the total number of ways in which these 5 friends can be seated
= Number of ways in which John can sit AND Number of ways in which the other 4 can sit
\(= 3 * 24\)
\(= 72\)
Hence, the correct answer is
Option D.
Thanks,
Saquib
Quant Expert
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