Question

Five persons are chosen at random from a group of ten persons consisting of four men and six women. Calculate the probabilities that the five persons chosen will

I. Consist of five women

ii. Consist of two women and three men

Answer 1

i.

$$P(5\ women)=\dfrac{\dbinom{6}{5}\dbinom{4}{0}}{\dbinom{10}{5}}=\dfrac{6(1)}{252}=\dfrac{1}{42}$$

ii.

$$P(2\ women\ \&\ 3\ men)=\dfrac{\dbinom{6}{2}\dbinom{4}{3}}{\dbinom{10}{5}}=\dfrac{15(4)}{252}=\dfrac{5}{21}$$