A group consists of fivefive men and fivefive women. ThreeThree people are selected to attend a conference. a. In how many ways can threethree people be selected from this group of tenten ? b. In how many ways can threethree women be selected from the fivefive women? c. Find the probability that the selected group will consist of all women.

a). Three people can be selected from a group of ten in

(10 · 9 · 8) = 720 ways.

(But every group of 3 different people can be selected in 6 different ways. So there are actually only (720/6) = 120 different groups of 3 different people.)

b). Three women can be selected from a group of five women in

(5 · 4 · 3) = 60 ways.

(But every group of 3 different women can be selected in 6 different ways. So there are actually only (60/6) = 10 different groups of 3 different women.)

c). Start with 3 men and 3 women.

The probability of the first selection being a woman is (3/6) = 50%.

Then there are 3 men and 2 women.

The probability of the 2nd selection being a woman is (2/5) = 40%.

Then there are 3 men and 1 woman.

The probability of the 3rd selection being a woman is (1/4) = 25%.

The probability of all 3 selections being women is

(50% ·40% ·25%) = (0.5 ·0.4 ·0.25) = 0.05

The probability that the selected group will consist of all women is 5%.