Find probability of having a female in every group 10 male students and 5 female students are split into 5 groups (every grup consists of 3 students). What is the probability that there is a female student in every group?
I should solve this with combinatorics. Any idea on how to appraoch the problem?

total possible: ${15\choose 3}{12\choose 3}{9\choose 3}{6\choose 3}{3\choose 3}$
one female in every group:  ${10\choose 2}{5\choose 1}{8\choose 2}{4\choose 1}{6\choose 2}{3\choose 1}{4\choose 2}{2\choose 1}{2\choose 2}{1\choose 1}$
solution: ${{10\choose 2}{5\choose 1}{8\choose 2}{4\choose 1}{6\choose 2}{3\choose 1}{4\choose 2}{2\choose 1}{2\choose 2}{1\choose 1}}\over{{15\choose 3}{12\choose 3}{9\choose 3}{6\choose 3}{3\choose 3}}$
