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) (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.
possible arrangements
(2)
Multiply all possible groupings of boys times
all possible groupings of girls
Then times 2, since they can switch sides
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 ways to seat the girls
for each of the 3 ways, so I have
so far
The boys can sit in different ways
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
ways so far
The boys can still be arranged in
different ways
possible seatings
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It wouldn't hurt to get other opinions, too
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