SOLUTION: 4 boys and 2 girls are sitting on a bench 1) what is the number of possible dispositions 2) same question if the boys are sitting on a side and the girls are on the other side

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Question 1062718: 4 boys and 2 girls are sitting on a bench
1) what is the number of possible dispositions
2) same question if the boys are sitting on a side and the girls are on the other side
3) same question if each girl is sitting between 2 boys
4) same question if the 2 girls want to sit next to each other
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
There can be a boy or a girl in any position,
so you can just regard them as people.
+1%2A2%2A3%2A4%2A5%2A6+=+720+ possible arrangements
(2)
Multiply all possible groupings of boys times
all possible groupings of girls
Then times 2, since they can switch sides
+%28+1%2A2%2A3%2A4+%29%2A%28+1%2A2+%29%2A2+=+96+ possible seatings
(3)
If you line up the 4 boys, there are only 3 ways
that 2 girls can sit between 4 boys:
b g b g b b
b b g b g b
b g b b g b
Also, there are +1%2A2+=+2+ ways to seat the girls
for each of the 3 ways, so I have
+2%2A3+=+6+ so far
The boys can sit in +1%2A2%2A3%2A4+=+24+ different ways
+6%2A24+=+144+ possible seatings
(4)
Here are the possible ways that 2 girls can sit next to each other:
g g b b b b
b g g b b b
b b g g b b
b b b g g b
b b b b g g
or, 5 different ways
The girls can swap positions, so there are
+2%2A5+=+10+ ways so far
The boys can still be arranged in
+1%2A2%2A3%2A4+=+24+ different ways
+10%2A24+=+240+ possible seatings
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It wouldn't hurt to get other opinions, too