10 balls are placed in 10 boxes independently at random. Assuming that all 10 boxes were initially empty, what is the expected number of boxes that remain empty? Here are the possible answers, but please explain the solution:
a)$\left(\frac{9}{10}\right)^9$
b)$\frac{9^9}{10^{10}}$
c)$\frac{9^{10}}{10^9}$
d)$\left(\frac{9}{10}\right)^{10}$
I guess that the answer is c) because the probability that box is empty is $(\frac{9}{10})^{10}$ and we should multiply it by 10 as there are 10 boxes.
