Question

Alejandra's DVD movie collection includes 4 horror selections, 4 science fiction, 3 drama, 3 thrillers, and 2 comedies. If she picks two DVD's for an evening, without replacing them, what is the probability she will pick two thriller selections?

Answer 1

$\displaystyle |\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\ |A|=\binom{3}{2}=\dfrac{3!}{2!}=3\\\\ P(A)=\dfrac{3}{120}=\dfrac{1}{40}=2,5\%$