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permutation & combination problem

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by abhinav khanna » Sun Apr 22, 2012 7:41 am
Hi all,

Kindly guide me to the solution to this problem

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?

Thanks
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by pemdas » Sun Apr 22, 2012 9:54 am
revised
abhinav khanna wrote:Hi all,

Kindly guide me to the solution to this problem

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?

Thanks
both can sit next to only one other student in the following cases:
case 1) both sit together and at the beginning of row
case 2) the same but at the end of row

in both cases we have to clue Bob and Lisa as one immovable object. We permute the other three students such as 3! along with Bob and Lisa will changing their place in 2 ways, hence 2*3!=12 ways

The total possibilities would be 2*12=24 ways.

what's OA? also I'm not sure the question was precisely formulated :( so I tried my best in 1.5 minutes
Last edited by pemdas on Sun Apr 22, 2012 10:03 am, edited 1 time in total.
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by abhinav khanna » Sun Apr 22, 2012 10:02 am
I too had the same problem with the language nevertheless you are correct. 48 is the answer but i need more guidance may be both of us are thinking on wrong lines.
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by minhchau1986 » Sun Apr 22, 2012 10:26 am
I wonder my answer is different from yours.
If both of them Sits next to other student, it means they sit together in the beginning of the row or the end of the row.

Blxxx 3 ways
Xxxbl 3 ways

6 in total. What did I do wrong?
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by aneesh.kg » Sun Apr 22, 2012 12:17 pm
The question is ambiguous. We can never have both B as well as L next to exactly one person.
So, maybe, the question wants the pair of B and L to be next to exactly one person.
In that case
B L _ _ _ and _ _ _ B L are the two possibilities. We also have to take into account the arrangement of B an L.
In each of the above pattern, three people on the three dashes can be arranged in 3! ways.

Required number of arrangements = (3! + 3!)*(2!)
= 24
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by pemdas » Sun Apr 22, 2012 2:20 pm
exactly, the text is imprecise :(
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