A group of 8 boys and 6 girls are to stand in a straight line for a photograph. In how many ways can these 14 children be arranged so that none of the girls stand next to each other?

Question

anonymous · Answer

$ \large ^9P_6 \times 8! = \cdots $

anonymous · Answer

@FoolForMath how did you get that?

anonymous · Answer

There are 9 places for 6 girls to go so that no girls would be together.

anonymous · Answer

2438553600

anonymous · Answer

but there are only 7 places available so that the girls are not together

anonymous · Answer

_B_B_B_B_B_B_B_B_

anonymous · Answer

two boys could be together too and yet the girls will be separated...

anonymous · Answer

_BB_B_B_B_B_B_B_