permutations with restrictions question

[riyakhilnani7]

What is the rationale behind the answer to this question

There are 6 children, 3 boys and 3 girls. They will be lined up single file for a photo, alternating genders. how many arrangements of children are possible?

Answer: 3! x 3! x 2 = 72

[garima_aries01]

There are 6 children, 3 boys and 3 girls. They will be lined up single file for a photo, alternating genders. how many arrangements of children are possible

B = boy
G = girl

BGBGBG ==>3 Bs can be placed in 3! ways
Likewise 3 Gs can be placed in 3! ways
And the sequence can be GBGBGB too so
2x3!x3!

[tim]

thanks! let us know if there are any further questions on this one..