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% .
