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# A group of 5 students bought movie tickets in one row next

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Intern
Joined: 16 Jan 2013
Posts: 24
Concentration: Finance, Entrepreneurship
GMAT Date: 08-25-2013
A group of 5 students bought movie tickets in one row next  [#permalink]

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Updated on: 12 Aug 2013, 03:05
4
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:04) correct 37% (01:37) wrong based on 197 sessions

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A group of 5 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the four other students from the group?

(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

Can somebody plz clarify that the answer to this prob is 4!*2 which I am getting, but the answer in the book is given something else.

Originally posted by Countdown on 12 Aug 2013, 02:40.
Last edited by Bunuel on 12 Aug 2013, 03:05, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: A group of 5 students bought movie tickets in one row next  [#permalink]

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12 Aug 2013, 03:05
1
1
Countdown wrote:
A group of 5 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the four other students from the group?

(A)5%
(B)10%
(C)15%
(D)20%
(E)25%

Can somebody plz clarify that the answer to this prob is 4!*2 which I am getting, but the answer in the book is given something else.

The question basically asks about the probability that Bob and Lisa sit at the ends.

The total # of sitting arrangements is 5!.

Desired arrangement is either BXYZL or LXYZB. Now, XYZ can be arranged in 3! ways, therefore total # of favorable arrangements is 2*3!.

P=(favorable)/(total)=(2*3!)/5!=1/10.

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Joined: 14 Dec 2012
Posts: 787
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6

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12 Aug 2013, 03:05
Countdown wrote:
A group of 5 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group,
what is the number of ways of seating if both of them will sit next to only one other student from the group?

Can somebody plz clarify that the answer to this prob is 4!*2 which I am getting, but the answer in the book is given something else.

LET SAY THAT BOB = B ..LISA = L
LET ONE OTHER GUY = X
NOW see question is saying....B AND L will sit next to this GUY only I.E X.
what you have done is you assumed that question is asking that B and L will sit together.
so according to given condition X cannot sit at the corner seat because in that case both B and L cant sit next to X.
so FOR X we can make hime arrange in 3!ways and B and L can be arranged in 2! ways.
therefore total ways = $$3!*2!$$

hope it helps.
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Joined: 10 Jul 2013
Posts: 315
Re: A group of 5 students bought movie tickets in one row next  [#permalink]

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12 Aug 2013, 10:53
1
1
Countdown wrote:
A group of 5 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the four other students from the group?

(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

Can somebody plz clarify that the answer to this prob is 4!*2 which I am getting, but the answer in the book is given something else.

use this diagram : it can help
Attachments

bob lisa.png [ 24.68 KiB | Viewed 3603 times ]

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Re: A group of 5 students bought movie tickets in one row next &nbs [#permalink] 12 Aug 2013, 10:53
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