Question

in how many ways 2 boys and 2 girl can stand in a row

Answer 1

bbgg
bgbg
gbgb
ggbb
bggb
gbbg so 6

Answer 2

Seems right. Is there a mathematical formula that could be used?

Answer 3

The 2 boys and 2 girls are simply 4 different people. You could call them b1, b2, g1 and g2.
There are 4 people to choose from for the first person in the row. Having chosen the first person in the row there are 3 choices of people for the second in the row. Therefore there are 4 * 3 choices for the first two people in the row. Continuing this reasoning the total number of ways of the four people to stand in a row is given by:
\[4\times3\times2\times1=factorial\ 4\ (4!)\]
Note: The number of permutations of n different things taken n at a time is n!

Answer 4

Well, that assumes the boys are distinguishable from one another
and the girls are distinguishable from one another, making

bbgg have: b1b2g1g2, b1b2g2g1, b2b1g1g2, and b2b1g2g1 = four
different ways itself, and so on for the others, like ggbb.

If this meant 4 distinguishable students then we have a b c d,
giving 4! permutations, but no reason to mention "two boys and two girls."

Perhaps the question is ambiguous.

Answer 5

I think that the question is framed to test whether students see past the gender difference. Note that even 'identical' twins are separate people, even though it could be very difficult to distinguish between them!

Answer 6

Egad. PC enters math?

Answer 7

lol.