Question 1033026: In how many ways can 2 boys and 5 girls be seated in a row, such that the boys do not sit together?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Method 1:
The number of ways of seating 7 people in a row of chairs w/o any restriction is 7!. The number of ways where the two boys are seated beside each other is 2*6!. Hence the number of ways of seating 5 girls and 2 boys such that the two boys don't sit next to each other is 7! - 2*6! = 5*6! = 3,600 ways.
Method 2:
First seat the five girls in a row. This can be done in 5! ways. After doing this, one boy can be inserted in any of the four spaces in-between the girls or the two end positions, or all-in-all 6 ways. The other boy can then be seated in any of the five remaining spaces (not beside the boy initially seated). This can be done in 5 ways. Hence there are 6*5*5! = 5*6! = 3,600 ways.
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