Well yes it matters, we are not talking about identical white and black balls

Now the solution

We know that the total number of kids = 6

Since boys can stand in the corners, we need to know specifically how many boys and girls are there.

Statement 1

If number of girls is 4 then number of boys = 2

This is sufficient to calculate the number of arrangements.

(Not required but I will go ahead and get the number of arrangements)

First we fill in the corners with 2 girls, can be done in 4*3 ways

Now we can arrange the remaining 4 kids in any order = !4

Total number of arrangements = 4*3*!4

Statement 2

there are 12 different ways to fill first and last spot

Let number of girls be n then number of ways to fill the corners= n*(n-1)

n*(n-1)=12

n=-3 or n=4

4 is the only possible value, we can solve as above to get the arrangements.

Answer is D.

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