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2 teachers and 3 students line up in a row. How many different arrange

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2 teachers and 3 students line up in a row. How many different arrange [#permalink]

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New post 27 Dec 2017, 01:04
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[GMAT math practice question]

2 teachers and 3 students line up in a row. How many different arrangements are possible if the teachers cannot be adjacent to each other?

A. 60
B. 72
C. 81
D. 90
E. 100
[Reveal] Spoiler: OA

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Re: 2 teachers and 3 students line up in a row. How many different arrange [#permalink]

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New post 27 Dec 2017, 04:56
MathRevolution wrote:
[GMAT math practice question]

2 teachers and 3 students line up in a row. How many different arrangements are possible if the teachers cannot be adjacent to each other?

A. 60
B. 72
C. 81
D. 90
E. 100



Hi..

place 3 students in a row with gaps........ _S_S_S_
so there will be 4 gaps as shown above, which can be filled up by 2 teachers
so 4C2*2! = 12
the 3 students can be seated in 3!=6 ways

total 12*6=72
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Re: 2 teachers and 3 students line up in a row. How many different arrange [#permalink]

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New post 27 Dec 2017, 05:05
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There are 2 teachers, 3 students => t1,t2,s1,s2,s3
_ _ _ _ _ (5 positions)

Total number of arrangements possible (without any condition) = 5! =120
Lets find the arrangement in which both teachers ARE together
t1 t2 s1 s2 s3
lets group t1 & t2 as one entity (to ensure they are together during the arrangements) and arrange
=> (t1 t2) s1 s2 s3
No=4! x 2! =48
2! because of t1,t2 & t2,t1.


Required number of arrangements = 5! - 4!*2! = 120 -48 = 72
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Re: 2 teachers and 3 students line up in a row. How many different arrange [#permalink]

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New post 28 Dec 2017, 22:55
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Since at least one student should be between the two teachers, we should consider complementary cases. This means we should calculate the difference between the total number of arrangements and the number of arrangements in which the teachers are adjacent to each other.


The total number of ways in which 5 people can stand in a row is 5!= 120.
The total number of arrangements with the teachers adjacent to each other is 4! * 2!.
Thus, the total number of permitted arrangements is 5! – 4! * 2! = 120 – 48 = 72.

Therefore, the answer is B.

Answer: B
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Re: 2 teachers and 3 students line up in a row. How many different arrange   [#permalink] 28 Dec 2017, 22:55
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