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# In how many ways can you seat 7 people on a bench if one of

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In how many ways can you seat 7 people on a bench if one of [#permalink]

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31 Oct 2013, 22:16
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Difficulty:

25% (medium)

Question Stats:

77% (02:33) correct 23% (01:33) wrong based on 124 sessions

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In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080
[Reveal] Spoiler: OA

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Arindam Sur

Last edited by arindamsur on 01 Nov 2013, 00:02, edited 2 times in total.
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Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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31 Oct 2013, 23:43
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Expert's post
arindamsur wrote:
In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080

Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 4 chairs to sit. The remaining 6 people can sit in 6! ways. Thus the # of arrangements is 4*6! = 2,880.

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Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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01 Nov 2013, 08:48
There are 7! total ways to sit everyone.

There are 3 seats that he can't sit in (the two ends and the middle). For each seat of the 3 seats he can't sit in, there are 6! arrangements of people in the other seats. So the total number of arrangements where he isn't sitting in any of those three seats is:

7! - 6!(3) =
6!(7 - 3) =
6!(4) =
2880
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Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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02 Nov 2013, 00:42
total no of ways in which all 7 can be seated = 7! ways

now,
if rohit sits at first seat then remaining 6 can be seated in 6! ways
if rohit sits at middle seat then remaining 6 can be seated in 6! ways
if rohit sits at last seat then remaining 6 can be seated in 6! ways

no. of ways in which rohit doesnt sits in middle or at either ends = 7! - (6! + 6! + 6!) = 7! - 6!*3 = 6!(7-3)=6!*4=2880

Hope this helps.
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Re: In how many ways can you seat 7 people on a bench if one of   [#permalink] 02 Nov 2013, 00:42
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