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A teacher has 15 students in his class, 8 girls and 7 boys. He wants to seat them in three rows of five, but knows that if any row has two girls or two boys sitting next to each other, they will talk and won't pay attention. How many seating arrangements can he make that avoid this?
 

 Apr 22, 2018
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A teacher has 15 students in his class, 8 girls and 7 boys. He wants to seat them in three rows of five, but knows that if any row has two girls or two boys sitting next to each other, they will talk and won't pay attention. How many seating arrangements can he make that avoid this?

 

one row must be   BGBGB

and 2 rows must be GBGBG

there are 3 combination for this.

 

Given just one of these three combinations  Lets place the girls.

8 positions, 8 girls, 8! permutation

For the boys there are 7! permutations.

 

So altogether I get   3*8!*7! 

 

3*8!*7! = 609 638 400 seating possibilities.

 Apr 22, 2018

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