Answer to Question #220260 in Statistics and Probability for Musenga sichona

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.

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