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# if there are 3 students and 2 teachers, and they have to be

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Intern
Joined: 20 Aug 2003
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if there are 3 students and 2 teachers, and they have to be [#permalink]  25 Aug 2003, 11:16
if there are 3 students and 2 teachers, and they have to be arranged in a straight line.how many arrangements can be made if the teachers have to be either at the front or the back on the line.
Intern
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why wouldn't it be 12?

2 ways the teachers can be arranged and 3! ways the students can be arranged-

2* 3!=12
Manager
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sure, but they can be either at the front or at the back...
Intern
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right that's why we're multiplying 2 with 3!...

i was getting confused b/w 12 and 24 for the same reason.

there are 2 ways to arrange the two teachers(front back, back front) and 3! ways to arrange the students for each way the teachers are arranged.

so it should be 2 * 3!

please tell me where am I going wrong?
Manager
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teachers at front: 2!*3!
teachers at back: 3!*2!
Intern
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Oh!

the way I was reading the questions was that either teacher has to be in the front and the back.

thanks a lot javropu!
Manager
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no problemo...
if the problem was
TTCCC or CCCTT then answer is 2*2!*3!
if the problem was
consecuently, if the problem was
TTCCC, CCCTT or TCCCT then answer is 24+12=36
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