SOLUTION: Please help me answer this word problem: If Mrs. Smith takes her class of 12 students to the theater. They sit in the front row where there is exactly twelve seats. There are 9 gir

Question 248523: Please help me answer this word problem: If Mrs. Smith takes her class of 12 students to the theater. They sit in the front row where there is exactly twelve seats. There are 9 girls and 3 boys. How many different ways can they be seated if the boys cannot sit next to eachother. Solve both independently and dependently.
I am not sure how to begin this problem.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me answer this word problem: Mrs. Smith takes her class of 12 students to the theater.
They sit in the front row where there is exactly twelve seats.
There are 9 girls and 3 boys.
How many different ways can they be seated if the boys cannot sit next to each other.
Solve both independently and dependently.
I am not sure how to begin this problem.
---------------------------------------------
There are 12C3 ways to place the boys without restriction.
-------------
There are 2*9 ways to place the boys if they all sit together.
-------------
If 2 boys sat together there would be 9 ways to place the 3rd
boy without the 3 sitting together. And 2 boys can sit together
in 11 ways. So there are 11*9 ways of having a 2 boy/1boy split.
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Your Problem:
If no boys can sit next to one another: 12C3-18-99 = 220-117 = 103 ways
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Cheers,
Stan H.

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