4 boys and 2 girls are sitting on the bench
1) what is the number of possible dispositions
6! = 720
2) same question if the boys are on a side and the girls are on the other side
2 ways to choose the general seating arrangement:
BBBBGG or GGBBBB
4! = 24 ways to arrange the boys
2! = 2 ways to arrange the girls
That's 2*24*2 = 96 ways.
3) same question if each girl is sitting between 2 boys
3 ways to choose the general arrangement:
BGBGBB, BGBBGB, or BBGBGB
4! = 24 ways to arrange the boys
2! = 2 ways to arrange the girls
That's 3*24*2 = 144 ways.
4) same question if the girls want to sit next to each other
5 ways to choose the general arrangement:
GGBBBB, BGGBBB, BBGGBB, BBBGGB, BBBBGG
4! = 24 ways to arrange the boys
2! = 2 ways to arrange the girls
That's 3*24*2 = 144 ways.
Edwin
