### Counting

4 men, 6 women, 3 spots to fill.

A) One man and two women
B) At least two men
C) At least one person of each sex

I can't get these, and I don't know why. My logic seems right, but it doesn't get the right answer.

A) Pick a man, 4 choices. Pick a woman, 6 choices, pick the other woman, 5 choices. 4 * 6 * 5 outcomes. This is wrong.
B) Pick a man, 4 choices. Pick another man, 3 choices. Pick the last person, 6 + 2 choices. 4 * 3 * 8 outcomes. Wrong.
C) Pick a male, 4 choices, pick a female 6 choices, pick the last, 5 + 3 choices. 4 * 6 * 8 outcomes. This is also wrong.

The hell is going wrong here? Have a final for this tomorrow and figured I'd brush up on my counting and I guess I just completely forgot how to do anything of this.
You're using the formula for permutations. You should be using the formula for combinations.

A) (4!/(1!*(4-1!))) * (6!/(2!*(6-2)!) = 4 * (6*5 / 2 ) = 4*15 = 60
Oh wow I don't know how I overlooked that. Figures it was just some simple issue. Thanks though
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