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$10$ people are entering an elevator at the first floor. The building has seven floors. $X$ is a random variable that represents number of stops of the elevator until all $10$ people leave the elevator. Find the distribution of $X$, $EX$ and $DX$.

I think that this is a binomial distribution: $\sum_{k=1}^{7}\binom{7}{k}(1-\frac{6^{10}}{7^{10}})^{k}(\frac{6^{10} }{7^{10}})^{7-k}$.

Then EX and DX are easily found: $EX=np, DX=npq$, where $n=7, p=1-\frac{6^{10}}{7^{10}}$ and $q=\frac{6^{10}}{7^{10}}$

Is this correct?

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Since my reputation isn't high enough to make a comment, I will use the answer field to give some direction. The number of possible outcomes is 1,2,3,4,5,6 stops. The people are entering at the first floor and have six floors to leave. The probability that every person leaves at one floor is $(\frac{1}{6})^{10}$.

RDS
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