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A group of 5 students bought movie tickets in one row next to each oth

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A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post Updated on: 26 Nov 2018, 22:13
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Question Stats:

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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%

Originally posted by bkk145 on 20 Jun 2007, 16:03.
Last edited by Bunuel on 26 Nov 2018, 22:13, edited 3 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 09 Sep 2013, 01:59
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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%

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.

Answer: B.
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 12 Aug 2013, 09:53
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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
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bob lisa.png
bob lisa.png [ 24.68 KiB | Viewed 4241 times ]


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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 20 Feb 2015, 12:41
2
Hi All,

There are several different 'math' approaches to this question. You have to be clear that there are 2 'acceptable' orientations of the 5 people though:

Bob, X, X, X, Lisa
Lisa, X, X, X, Bob

Since either Bob OR Lisa would have to be in the 'first spot', there's a 2/5 probability of that happening....

That would leave the other person to occupy the 'fifth spot'; since there are 4 people remaining, there's a 1/4 probability of that happening....

(2/5)(1/4) = 2/20 = 1/10 = 10%

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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 21 Feb 2015, 22:26
"what is the probability that Bob and Lisa will each sit next to only one of the four other students from the group?"

Can someone please explain why the arrangement can't be " _ B _ L _ " or " _ L _ B _ "?
Does this not also satisfy that B & L also sit next to the other four students?
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 21 Feb 2015, 22:41
1
Hi icetray,

The prompt tells us that the 5 seats are in a row. For Bob/Lisa to sit next to JUST 1 student, they would both have to sit on the ENDS of the row. In the examples that you listed, Bob and Lisa are sitting next to 2 students, which does not fit the "restrictions" of what we're asked to deal with.

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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 07 Sep 2016, 19:29
1
There are 2 different ways this can happen

LxxxB or BxxxL

Here is the probability of this happening (1/5)(3/4)(2/3)(1/2)(1/1)=2/20 or 1/10 10%
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 17 Oct 2016, 01:04
Hi all,
I have a problem with the question.
what is the probability that Bob and Lisa will each sit next to only one of the four other students.
Is the question saying that Bob and Lisa will sit at the extremes. However, I solve it treating subgroup like (B _ L) X X X and then solve for possible arrangement and got the same answer. But the official answer says that Bob and Lisa sat at the extremes. Is my understanding wrong?
Help me.
TIA
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 17 Oct 2016, 13:04
NaeemHasan wrote:
Hi all,
I have a problem with the question.
what is the probability that Bob and Lisa will each sit next to only one of the four other students.
Is the question saying that Bob and Lisa will sit at the extremes. However, I solve it treating subgroup like (B _ L) X X X and then solve for possible arrangement and got the same answer. But the official answer says that Bob and Lisa sat at the extremes. Is my understanding wrong?
Help me.
TIA


Hi NaeemHasan,

In the example that you listed, Lisa is sitting next to TWO people - and that is not in line with what the question states.

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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 19 Oct 2016, 01:23
EMPOWERgmatRichC wrote:
NaeemHasan wrote:
Hi all,
I have a problem with the question.
what is the probability that Bob and Lisa will each sit next to only one of the four other students.
Is the question saying that Bob and Lisa will sit at the extremes. However, I solve it treating subgroup like (B _ L) X X X and then solve for possible arrangement and got the same answer. But the official answer says that Bob and Lisa sat at the extremes. Is my understanding wrong?
Help me.
TIA


Hi NaeemHasan,

In the example that you listed, Lisa is sitting next to TWO people - and that is not in line with what the question states.

GMAT assassins aren't born, they're made,
Rich

Hi,
How? I allow only one person to sit between Bob and LIsa. Does this mean they sit next to two people? If so, Could you elaborate this, please.
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 19 Oct 2016, 19:57
2
Hi NaeemHasan,

In the example: B _ L _ _ _

Bob is sitting next to one person and Lisa is sitting next to two people.

The prompt asks for the probably that both Bob and Lisa will sit next to ONE person... NOT that Bob and Lisa will sit next to the SAME person. When sitting in a row of 6 people, the only way to sit next to just one person is to sit on the 'end' of the row. Thus, there are only two possible outcomes that meet this restriction:

B _ _ _ _ L
L _ _ _ _ B

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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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New post 12 Nov 2017, 06:39
1
What I understand is that Bob and Lisa should have only person sitting next to them, this implies they take the edge seat
So total arrangement=5!=120
now the arrangement to meet the condition=3!2!( Arranging Bob and Lisa on edge seat=2!, Arranging the rest=3!)
So probability= 3!2!/5!=1/10=10%
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Re: A group of 5 students bought movie tickets in one row next to each oth  [#permalink]

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Re: A group of 5 students bought movie tickets in one row next to each oth &nbs [#permalink] 26 Nov 2018, 22:13
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