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John and four friends go to a Lakers game. In how many ways can they

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John and four friends go to a Lakers game. In how many ways can they  [#permalink]

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New post 19 Feb 2017, 10:50
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A
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D
E

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Question Stats:

66% (01:27) correct 34% (01:25) wrong based on 73 sessions

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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
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Re: John and four friends go to a Lakers game. In how many ways can they  [#permalink]

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New post 19 Feb 2017, 11:10
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5! is the number of ways to place the five people => 120

There is two impossible case when John sit in the left and in the right => Therefore the number of possible case is 3

120 * 3/5 (the probability of possible case)= 72 => Answer D
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Re: John and four friends go to a Lakers game. In how many ways can they  [#permalink]

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New post 19 Feb 2017, 12:19
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.

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Re: John and four friends go to a Lakers game. In how many ways can they  [#permalink]

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New post 24 May 2019, 20:54
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Re: John and four friends go to a Lakers game. In how many ways can they   [#permalink] 24 May 2019, 20:54
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