There are 5 men and 3 women. Company is hiring to fill four managerial vacancies.
Probability that at least one woman will be selected = 1 - Probability that no woman is selected
Probability that no woman is selected = \(\frac{^5C_4 \times ^3C_0}{^8C_4}=\frac{5\times 1}{70}=\frac{5}{70}\)
Probability that at least one woman will be selected = 1 - Probability that no woman is selected = 1 - (5/70) = 65/70 = 0.93