Question 979302
How many different pairs of advisors can you form from {{{3+7=10}}} professors?
You can form {{{10*9/2=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*6/2=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 {{{21/45=7/15}}} of all the possible sets of two professors that could be advisors.
So, the probability that both professors are chemistry professors is
{{{7/15=about}}}{{{0.467=about}}}{{{"46.7%"}}}