I'm having trouble with a probability question. It goes, "a class room has three rows of 4 seats. These 12 seats are randomly assigned to 4 male students and 5 female students. a)What is the probability that no female student sits in the front row?"
What I've tried to do is divide 8 choose 5 by 12 choose 9. But that isn't the answer. Apparently the answer is 7/99 and I've got no idea how the book got there.
Can someone please explain to me how to do it? Can you not only show me the solution, but also explain to me, how you got there? Thanks.
The correct answer is:$$\frac{\binom85\binom40}{\binom{12}5}=\frac{\binom85}{\binom{12}5}$$
You only have to focus on females and this is the probability that $5$ chairs are selected for them that do not belong to the front row.