Probability 3 women will end up on same team drawing from 20 people (3 women/17 men)

There are 20 people and we are forming 2 teams of 10 people. 3 of the people (3/20) are women (17 are men). Names are drawn from random, in alternating order for teams. What is the probability that all 3 women end up on the same team?

Initially I thought it was 25%...1st women has 100% chance, next woman has 50% chance and finally 3rd woman has 50% chance so .5*.5 =.25
Then I thought it could be 17 choose 10/20 choose 10 = 0.105 or possibly 2 * 0.105

Any help?

steve212 said:

There are 20 people and we are forming 2 teams of 10 people. 3 of the people (3/20) are women (17 are men). Names are drawn from random, in alternating order for teams. What is the probability that all 3 women end up on the same team?

Initially I thought it was 25%...1st women has 100% chance

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The "1st wom[a]n has" a "100% chance" of what?

steve212 said:

next woman has 50% chance and finally 3rd woman has 50% chance so .5*.5 =.25

Click to expand...

The "next woman has" a "50% chance" of what?

If the "3rd woman has" a "50% chance" (of what?), why is her probability 25%?

steve212 said:

Then I thought it could be 17 choose 10/20 choose 10 = 0.105 or possibly 2 * 0.105

Click to expand...

By what reasoning?

Please be specific. Thank you!