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# In how many different ways can 4 teachers and 4 students sit

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Intern
Joined: 06 Apr 2004
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In how many different ways can 4 teachers and 4 students sit [#permalink]  01 Jun 2005, 03:38
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In how many different ways can 4 teachers and 4 students sit around the table so that only 1 student can be placed between 2 teachers?

a)210 b)180 c)160 d)144 e)120

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Dan wrote:
I'll go for d.

(4-1)! * 4! = 144.

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since it is a circular perm, teachers can be arranged in (4-1)! Once this is done, students can be arranged 4! ways in between.

total arrangements = (4-1)! * 4!
Intern
Joined: 06 Apr 2004
Posts: 40
Followers: 0

Kudos [?]: 0 [0], given: 0

Dan wrote:
since it is a circular perm, teachers can be arranged in (4-1)! Once this is done, students can be arranged 4! ways in between.

total arrangements = (4-1)! * 4!

Thanks, Dan. Initially, I thought teachers and students can be regarded as 1 person in the following pattern: TS TS TS TS. Then, permutation would be 3!*2*2*2*2. What's wrong with this approach?

By the way, the OA is D.
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