Question

A researcher randomly selects 8 adults from a group of 12 women and 15 men to do a study. Find the probability of selecting exactly 5 women and 3 men (without replacement)

Answer 1

The probability is 728/4485.

Setting up combinations for this, we have:
$\frac{_{12}C_5\times_{15}C_3}{_{27}C_8} \\ \\=\frac{\frac{12!}{5!7!}\times\frac{15!}{3!12!}}{\frac{27!}{8!19!}} \\ \\=\frac{792\times455}{2220075}=\frac{360360}{2220075}=\frac{728}{4485}$