Question: 2014 Fall Midterm - 16
Consider 10 boxes and 10 balls. We throw each ball, uniformly, in a random box. What is the probability that, after we have thrown all 10 balls, none of the 10 boxes is empty?
a) $\frac{10!}{10^{10}}$
b) $\frac{10^{10}}{10!}$
c) $1 - \frac{10 \cdot (9/10)^{10}}{10^{10}}$
d) None of the above.
Consider 10 boxes and 10 balls. We throw each ball, uniformly, in a random box. What is the
probability that, after we have thrown all 10 balls, none of the 10 boxes is empty?
(a)
$\frac{10^{10}}{10!}$
(b)
$1 - \frac{10 \cdot (9/10)^{10}}{10^{10}}$
(c)
None of the above.
(d)
$\frac{10!}{10^{10}}$