Kindly help me to answer this:
Suppose five integers are chosen successively at random between 0 and 13, inclusive. Find the probability that:
(Round your answer to four decimal places if necessary.)
a. they are all different
b. not more than 2 are the same?
The first can be anything. The chance the second does not match the first is $\frac {13}{14}$, then the chance the third does not match either is $\frac {13}{14}$ and so on, giving a chance of no match as $\frac {13\cdot 12 \cdot 11 \cdot 10}{14^4}$
For the second, compute the chance of exactly one match then add to the first. You can choose the locations of the match in ${5 \choose 2}=10$ ways. You have $\frac 1{14}$ chance that those locations match, then $\frac {13\cdot 12 \cdot 11 }{14^3}$ chance the other three are different from the one at those locations and each other. The chance comes out the same, so you can just double the first result.