Problem Solving

If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?
12
36
72
180
720

ANS is C, but explanation written:
Since we must alternate between boys & girls as we fill the seats,boys may either occupy seats 1,3,5 or seats 2,4,6
BGBGBG or GBGBGB
under first condition 3!=6 for boys and 3!=6 for girls, total 6x6=36
under second condition it is the same 36,
Total 36+36=72
!!!But, it the question it is not stated that we must alternate between boys and girls, there only stated that boys sould not sit beside one another,
thus arrangements like
BGGBGB, BGBGGB are possible, which are not written in the expl.
under this condition the answer has to be more than 72.

yes..i think that answer should be 4*3!*3!

hemanth28 wrote:yes..i think that answer should be 4*3!*3!

Hemanth, I'd really appreciate it if you can explain your answer further... why times it by 4? Thanks

Sonia

its 4 times because of the 4 combos possible....
bgbgbg
gbgbgb
bggbgb
bgbggb
and int multpild by 3! * 3! cos of the permutations of the byos and girls..