Question

A committee consists of 10 women and 7 men. Three members are chosen as officers. What is the probability that all three officers are women?.

Answer 1

`(3)/(17)`

Explanation:

The probability the first officer is a woman is
`(10)/(17)`.

The probability the second officer is a woman given the first officer is a woman is
`(9)/(16)`.

The probability the third officer is a woman given the first two officers are women is
`(8)/(15)`.

So, the probability is:

`(10)/(17) \cdot (9)/(16) \cdot (8)/(15)=(3)/(17)`