SOLUTION: Three statistics professors and seven chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advis

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Question 979302: Three statistics professors and seven chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advisors. If each professor has an equal chance of being selected, what is the probability that both professors are chemistry professors?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
How many different pairs of advisors can you form from 3%2B7=10 professors?
You can form 10%2A9%2F2=45 different two-professor sets advisors.
How many of those 45 different sets advisors have two chemistry professors?
How many different pairs of chemistry professors can you form from 7 chemistry professors?
You can from 7%2A6%2F2=21 sets of two chemistry professors.
What fraction of the 45 sets of possible advisors are those 21 sets of two chemistry professors?
They are 21%2F45=7%2F15 of all the possible sets of two professors that could be advisors.
So, the probability that both professors are chemistry professors is
7%2F15=about0.467=about%2246.7%25%22