It looks like a permutation problem, actually, right? The order matters so I'd say it's a permutation.

pharmxanthan wrote:In how many arrangements can a teacher seat 3 girls and 3 boys
in a row of 6 seats if no two children of the same gender are to
be adjacent?
(A) 6
(B) 12
(C) 36
(D) 72
(E) 144

OA is D.

first seat can be taken by any 6 of the children: so probability for 1st place is 6.
second seat can be taken by only 3 children of the opposite gender than the 1st place: so 3
third seat can again be taken by the same gender of the first place, therefore 2
fourth seat can be taken by the same gender as the second seat: therefore 2
fifth and sixth seat can be taken by 1 child of each gender.

so total probability is: 6*3*2*2*1*1= 72.

Preet

a combination problem is one in which order does not matter..
here the ordering is imp so it will be permutation problem


boys can be arranged in 3! ways
girls can be arranged in 3! ways
line can start either with a boy or girl..so 2 arrangements are possible

2*3!*3!=72

pharmxanthan wrote:In how many arrangements can a teacher seat 3 girls and 3 boys
in a row of 6 seats if no two children of the same gender are to
be adjacent?
(A) 6
(B) 12
(C) 36
(D) 72
(E) 144

OA is D.

outreach wrote:a combination problem is one in which order does not matter..
here the ordering is imp so it will be permutation problem

The order matters as we need to have boys and girls on alternate seats.

But here the order in which 3 boys will seat among themselves does not matter. So is the case for 3 girls. So, do we regard this problem as permutation or combination one?

pharmxanthan wrote:

outreach wrote:a combination problem is one in which order does not matter..
here the ordering is imp so it will be permutation problem

The order matters as we need to have boys and girls on alternate seats.

But here the order in which 3 boys will seat among themselves does not matter. So is the case for 3 girls. So, do we regard this problem as permutation or combination one?

Hi,

the order also matters within the boys and girls - otherwise the answer would be 2 (bgbgbg and gbgbgb).

Whenever you're arranging people, order matters, so use permutations.
When you're just selecting people and order doesn't matter, use combinations.

In this case we're figuring out exactly which child sits on each sit, so order is definitely a factor.

This is extremely similar to an ETS Gmat Powerprep 2 CAT Question
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?
A)6
B)9
C)12
D)36
E)720

3 girls and 3 boys can sit in 3! * 3! ways.

two different positions can be occupied by g1or b1.

thus 2* 6*6 - 72