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How many different can 2 students be seated in a row of 4

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prasannar
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How many different can 2 students be seated in a row of 4 [#permalink] New post   21 Feb 2008, 07:55
How many different can 2 students be seated in a row of 4 desks,so that there is always at least one empty desk between the students.

A-2
B-3
C-4
D-6
E-12

I was doing this problem, and made a silly mistake, wanted to share a simple and good problem with you.



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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   21 Feb 2008, 08:31
3*2 = 6

a _ _ b
a _ b _
_ a _ b

reverse the students
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   21 Feb 2008, 21:28
Yup, 6 is right

Thanks
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   22 Feb 2008, 22:54
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prasannar wrote:
How many different can 2 students be seated in a row of 4 desks,so that there is always at least one empty desk between the students.

A-2
B-3
C-4
D-6
E-12

I was doing this problem, and made a silly mistake, wanted to share a simple and good problem with you.


There are 4!/2! = 12 ways to arrange them. So to arrange the number of ways which there isnt a desk is simply 3! b/c we just count ab (the two students) as 1 unit. So 12-6 = 6
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   23 Feb 2008, 06:11
1
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This case is similar to the one to find out the number of different words made up of given four letters, among which two letters are same.
In how many ways can WRRT be arranged to form different words if WT don't be together.

The total number of ways, WRRT can be arranged= 4!/2! =12
There are 6 ways to arrange WRRT so that WT won't come together.
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   25 Feb 2008, 21:57
vshaunak@gmail.com wrote:
This case is similar to the one to find out the number of different words made up of given four letters, among which two letters are same.
In how many ways can WRRT be arranged to form different words if WT don't be together.

The total number of ways, WRRT can be arranged= 4!/2! =12
There are 6 ways to arrange WRRT so that WT won't come together.


permute 2 ppl across 4 seats = 4p2 = 4!/2! = 12

how did u get 6 for the second part?
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   26 Feb 2008, 01:17
I'd just draw it out

X Y
X Y
X Y

and reverse X/Y. 6.
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vshaunak@gmail.com
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   26 Feb 2008, 19:38
bmwhype2 wrote:
vshaunak@gmail.com wrote:
This case is similar to the one to find out the number of different words made up of given four letters, among which two letters are same.
In how many ways can WRRT be arranged to form different words if WT don't be together.

The total number of ways, WRRT can be arranged= 4!/2! =12
There are 6 ways to arrange WRRT so that WT won't come together.


permute 2 ppl across 4 seats = 4p2 = 4!/2! = 12

how did u get 6 for the second part?


No. of ways to seat W and T so that they don't sit together:

WRTR - 2 ways as W and T can interchange their positions
WRRT - 2 ways (same as above)
RWRT- 2 ways (same as above)
Total = 6ways
Hope I answered your question.
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Re: How many different can 2 students be seated in a row of 4 [#permalink] New post   26 Feb 2008, 19:51
gmatblackbelt gave me an alternative approach.

it is lumping (AB)XX and permuting those 3 elements. 3!/2! = 3
then permuting the subset 3*2! = 6



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Re: How many different can 2 students be seated in a row of 4 [#permalink]
26 Feb 2008, 19:51
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