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

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

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05 Dec 2004, 06:16
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In a certain movie theater, 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. 1,440
D. 5,040
E. 10,080
Director
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05 Dec 2004, 06:55
Is it C?

The first person has two choices: seats on either end of the row.

The remaining 5 can be seated 6P5 ways.

2*6P5 = 2*720 = 1440
Senior Manager
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05 Dec 2004, 11:16
ninomoi wrote:
ruhi160184 wrote:
C.. 6!*2

Can u pls explain?

They can occupy the 7 seats in the following manner:

123456 or

234567 ( since the aisle seat always needs to get ocupied)

Hence, this can be done in 6! ways.. since we are considering two possibilities, its 6!*2 OR 6!+6!
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05 Dec 2004, 16:58
ruhi160184 wrote:
ninomoi wrote:
ruhi160184 wrote:
C.. 6!*2

Can u pls explain?

They can occupy the 7 seats in the following manner:

123456 or

234567 ( since the aisle seat always needs to get ocupied)

Hence, this can be done in 6! ways.. since we are considering two possibilities, its 6!*2 OR 6!+6!

You and gayathri have the same result, but I believe you each
interpreted the problem differently.

"One of them needs to sit in a seat along the aisle. "

I and gayathri interpreted this statement as there is
one particular person who must sit in one of the two aisle
seats. After that one person is assigned to an aisle seat,
there are 6 seats left for the 5 people. This interpretation
puts all six people in the row, but allows for an empty
seat between two of the friends (in other words, both
aisle seats can be occupied).

Unless I misunderstood your explanation, you are assuming that
there can be no empty seat between the friends occupying
the aisle and that any one of the six friends may be the
one on the aisle. These assumptions offset each other and
produce the same value of 1440.
Director
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06 Dec 2004, 08:19
Excellent reading Richie. Right explanation. C is the OA.
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06 Dec 2004, 10:59
Yes you are right Richie. That was my basic assumption. Since 6 out of 7 seats can be occupied, one seat has to remain empty always. So I chose thos method as it is shorter.
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06 Dec 2004, 10:59
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