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

Question

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.

bmwhype2 · Answer

3*2 = 6

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

reverse the students

prasannar · Answer

Yup, 6 is right

Thanks

GMATBLACKBELT · Answer

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

vshaunak@gmail.com · Answer

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.

bmwhype2 · Answer

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

how did u get 6 for the second part?

StartupAddict · Answer

I'd just draw it out

X Y
X Y
 X Y

and reverse X/Y. 6.

vshaunak@gmail.com · Answer

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.

bmwhype2 · Answer

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

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

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