in a row so that each girl is in between 2 boys

1.	in a row so that each girl is in between 2 boys
Answer» For each of the 3 girls to be seated between 2 boys, the minimum number of boys needed is 4. The arrangement in which this happens is: BGBGBGB Since there are 5 boys, there is one boy left over, who can be placed next to any of the 4 boys already placed. So there are 4 possible arrangements if each child is identified only by their gender. They are: BBGBGBGB BGBBGBGB BGBGBBGB BGBGBGBB If each child is distinguishable (not identified only by their gender) then the number of possible arrangements is (4) x (5!) x (3!) = 4 x 120 x 6 = 2,880.

Answer»

For each of the 3 girls to be seated between 2 boys, the minimum number of boys needed is 4. The arrangement in which this happens is:

BGBGBGB

Since there are 5 boys, there is one boy left over, who can be placed next to any of the 4 boys already placed. So there are 4 possible arrangements if each child is identified only by their gender. They are:

BBGBGBGB

BGBBGBGB

BGBGBBGB

BGBGBGBB

If each child is distinguishable (not identified only by their gender) then the number of possible arrangements is

(4) x (5!) x (3!)

= 4 x 120 x 6

= 2,880.

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