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# In a certain movie theatre, the rows are 7 seats across with

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In a certain movie theatre, the rows are 7 seats across with [#permalink]

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08 Jan 2006, 13:58
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In a certain movie theatre, the rows are 7 seats across with aisles on either side. A group of 6 friends goes to the movies and finds an empty row to sit in. One of them needs to sit in a seat along the aisle. Which of the following calculations represents the number of possible different seating arrangements for the 6 friends?

A. 360
B. 720
C. 1440
D. 5040
E. 10,080

I chose D.

1st person can choose from 7 available seats. The next person has 6 seats to choose from and so on. So the number of seating arrangements is 7x6x5x4x3x2 = 5040.

But the answer is C. I dont understand why.

Thanks
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08 Jan 2006, 14:25
It is C.

Out of 7 people 1 of them has to be on an aisle. He can occupy either of the aisles. So there are two sets of possibilities depending on his seating.

Total = 2 * Number of ways in which 5 people can be seated in 6 chairs.
= 2 * 6! (empty seat can be also considered as an element in the arrangement)
= 1440.

HTH.
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08 Jan 2006, 16:11
Thanks Giddi!

I understood the question wrong. I assumed that any one of the six friends could sit along the aisle rather than one particular person.
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08 Jan 2006, 18:15
Out of 7 seats, 1 is permanantly occupied. Now we just need to assign 1 seat to the remaining 5, and there're 6P5 ways = 720. But we have another row on the other side of the aisle, so total # of ways = 1440
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09 Jan 2006, 00:26
yups it has to be C.
One guy has 2 options to sit on either side of aisle

rest 6 seats means 6!=720
Total=720*2=1440
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18 Jan 2006, 11:02
agree with C though i tripped on 6!( did not * by 2 for either side)
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