Question

Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that none are women?

Answer 1

Answer:
`\bold{(1)/(99)}`

Explanation:

There are 5 men and 7 women, which is a total of 12 people. Finding the probability that none of the four people are women is the same as saying that all four people are men.

`(5\ men)/(12\ total\ people)\ and\ (4\ men\ remaining)/(11\ people\ remaining)\ and\ (3\ men)/(10\ people)\ and\ (2\ men)/(9\ people)\\\\\\=(5* 4* 3* 2)/(12* 11* 10* 9)\\\\=((4* 3)* (2* 5))/(12* 11* 10* 9)\\\\=(1)/(11* 9)\\\\=(1)/(99)`