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# If ten students appear in an examination and 4 of them are

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Director
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If ten students appear in an examination and 4 of them are [#permalink]

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06 Jan 2004, 16:14
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?
Director
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06 Jan 2004, 16:30
If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

If it were a computer adaptive test then it would be 10!

If it were paper and pencil it would be 6!x4!
Senior Manager
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06 Jan 2004, 16:33
I feel the answer should be 6! * 4! * 4
Director
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06 Jan 2004, 16:57
If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

I'm a little confused now, there are only 5 spaces between 6 students. I'm not in my right mind today - stressful day in the markets for me.
Director
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06 Jan 2004, 17:05
Titleist wrote:
If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

I'm a little confused now, there are only 5 spaces between 6 students. I'm not in my right mind today - stressful day in the markets for me.

Director
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06 Jan 2004, 17:29
I agree with Geethu - I get 6!*4!*4
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06 Jan 2004, 22:36
Explanation Titleist & Geethu for ur answers

Vivek
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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07 Jan 2004, 09:04
Lets assume S as six different subject students and M as Math students. There are four different ways to arrange them.

M S M S M S M S S S

S M S M S M S M S S

S S M S M S M S M S

S S S M S M S M S M

S can be arranged in 6! ways and
M can be arranged in 4! ways

So, the answer should be 6! X 4! X 4
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07 Jan 2004, 09:52
Geethu wrote:
Lets assume S as six different subject students and M as Math students. There are four different ways to arrange them.

M S M S M S M S S S

S M S M S M S M S S

S S M S M S M S M S

S S S M S M S M S M

S can be arranged in 6! ways and
M can be arranged in 4! ways

So, the answer should be 6! X 4! X 4

You can also have more staggered patterns which would mean that the multiplier can be more than 4:

M S S M S S M S M S

S M S M S M S M S S x 2

S S M S M S M S M S x 2

S S S M S M S M S M x 2

M S M S M S M S S S

M S S M S M S M S S

M S S S M S M S M S

M S S S S M S M S M

M S S S M S S M S M

As you can see there are quite a few patterns here.

You can arrange them as long as the math students are not sitting next to each other. There was no limit on the question.

hmmm...
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07 Jan 2004, 10:25
Yes. You are right Titleist. So, what is the maximum number of possible combinations.
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09 Jan 2004, 21:35
subtract number of ways in which atleast two are together from the total number of ways.

if 2 are together then we have 4C2 and treating this as one group we have 8 people left so number of ways = 4C2 * (8+1)!
smilarly 3 people together = 4C3 * (7+1)!
and 4 people together = 4C4 * (6+1)!

total ways in which copying takes place =
4C2 * 9! + 4C3 * 8! + 4C4 * 7! = 7! * 465
subtract this from 10!
so we get
7! ( 10*9*8 - 465 ) = 255 * 7!

what is the official answer ?
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