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I just want a confirmation that I'm doing this right

There is a 10-floor building, 4 people get in the elevator in the ground floor and each gets off at one of the floors randomly and independently.

a)what's the probability that they all exit at different floors.

well it's $\frac{10*9*8*7}{10^4}$

b)two get off and only two get off at the same floor.

after a bit of thinking I found that it's $\frac{{4 \choose 2}*10*9^2}{10^4}$

Am I right ?

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    a) is correct, and I think you're on the right track for b). But the way you currently have it, you could have two people get off on floor 2 AND two people get off on floor 3. Due to the way the question is worded, I can't tell which is correct, but you might need to change $9^2$ to $9\cdot 8$. Does that make sense? – 2017-02-19
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    let me rephrase the question b) exactly two get off at the same floor. Is that clear enough? – 2017-02-20
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    @knrumsey now I get it why I'm wrong since exactly only two get off at the same floor the remaining two must get off at two different floor so it's $9*8$ not $9^2$ thank you. – 2017-02-20

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