What is the probability that all three prizes go to women?

Question

Party guests are each given a number at the door when they come in and during the party 3 numbers will be chosen at random from a hat to win door prizes. There are 20 people at the party of which 10 are women and 10 are men.

If the answer is not an integer, enter it as a fraction in simplest form.

Answer 1

C(x,y) = number of ways to choose y elements out of x total

x!

----

y! (x-y)!

how many ways to choose 3 women out of 10 = C(10,3)

how many ways to choose 0 men out of 10 = C(10,0)

how many ways to choose 3 women out of 10 and 0 men out of 10 = C(10,3)*C(10,0)

how many ways to choose 3 people out of 20 = C(20,3)

probability will choose 3 women out of 10 and 0 men out of 10

C(10,3)*C(10,0)/C(20,3)