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# In how many ways can 4 arts students and 4 science students

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In how many ways can 4 arts students and 4 science students [#permalink]

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22 Feb 2004, 09:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In how many ways can 4 arts students and 4 science students be arranged alternately round the table.
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22 Feb 2004, 10:17
Assuming that the students are distingushable,
then it is 7!.
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22 Feb 2004, 11:16
XAXAXAXAX- A can sit in 3! and S can occupy 5 places or 4! ways for S students seating, so i would go with 3!x4!=144.
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22 Feb 2004, 14:52
Assuming that the students are distingushable,
then it is 7!.

It is either 4!*3! or 7*4!*3! . But I feel it is 7*4!*3!
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22 Feb 2004, 19:34
Explanation:
Assuming A_B_C_D_ for art students positions and _E_F_G_H for science students. There are (4-1)! ways of sitting art students around the table and (4-1)! ways of sitting science students around the table. Also, there are 4C1 way for any given group's student to sit between any member of the other group. For instance, E could be between A/B or between B/C or between C/D or right after D. Therefore, answer is 3! * 3! * 4C1 = 144. Good job guys!
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22 Feb 2004, 20:00
Paul wrote:
Explanation:
Assuming A_B_C_D_ for art students positions and _E_F_G_H for science students. There are (4-1)! ways of sitting art students around the table and (4-1)! ways of sitting science students around the table. Also, there are 4C1 way for any given group's student to sit between any member of the other group. For instance, E could be between A/B or between B/C or between C/D or right after D. Therefore, answer is 3! * 3! * 4C1 = 144. Good job guys!

I agree with your answer but the explanation does not make sense.

Let's put student A as our point of reference and anchor her to the 1st position on the table. There are now 3 available positions at the table specifically for art sutdetns 4 avaibable position for the science student. Hence, there are 3! x 4! difference distinct arrangements of the "kichen sind athors)
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22 Feb 2004, 21:06
AkamaiBrah wrote:
I agree with your answer but the explanation does not make sense.

Let's put student A as our point of reference and anchor her to the 1st position on the table. There are now 3 available positions at the table specifically for art sutdetns 4 avaibable position for the science student. Hence, there are 3! x 4! difference distinct arrangements of the "kichen sind athors)

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23 Feb 2004, 14:56
4 Arts and 4 Science
3!*2! * 3!*2!

Ways to sit 4 Arts students is (4-1) = 3!. Now you can have this in 2 ways
so total is 3!2! = 12
same for science = 12

total = 12*12=144

I have multiplied 2! in both cases because both set of students have two seperate arrangements.

One which starts with arts student: A S A S A S A S
and One which starts with science student: S A S A S A S A

so both groups of arts and science students can be seated in 2! ways respectively
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23 Feb 2004, 21:53
pakoo wrote:
4 Arts and 4 Science
3!*2! * 3!*2!

Ways to sit 4 Arts students is (4-1) = 3!. Now you can have this in 2 ways
so total is 3!2! = 12
same for science = 12

total = 12*12=144

I have multiplied 2! in both cases because both set of students have two seperate arrangements.

One which starts with arts student: A S A S A S A S
and One which starts with science student: S A S A S A S A

so both groups of arts and science students can be seated in 2! ways respectively

I'm sorry, but your explanation does not make sense to me.
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24 Feb 2004, 07:40
Thanks for the solution AkamaiBrah. I understand what you mean.

Consider just the arts students first. They can be seated in a circle in (4-1)! = 3!

Now there are 4 empty places in between each Arts students and each of these empty places needs to be filled with a science student. 4 places and 4 science students. Thus, 4! ways

Total no. of ways = 3! x 4! = 144 (Answer)
24 Feb 2004, 07:40
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