Question

A small business employs 7 women and 3 men. The manager randomly selects 3 of them to be on a team. What is the probability that all 3 are women?

Answer 1

Answer: the answer would be 7/24

Explanation:

Answer 2

There are 10 employees all together.

-- The probability of selecting a woman first is 7/10 .
Then there are 6 women left, and 9 total.

-- The probability of selecting a woman second is 6/9 .
Then there are 5 women left, and 8 total.

-- The probability of selecting a woman third is 5/8 .

So the probability of all three selections is

(7/10) x (6/9) x (5/8)

= (7 x 6 x 5) / (10 x 9 x 8)

= 210 / 720

= 7 / 24 = about 29.2% .