Suppose we draw three balls out of an urn that contains 15 balls numbered 1 to 15. Let X be the largest number drawn. Find the probability function of X.

What I've got:

$\displaystyle For i>2, P(X=i) = \frac{(i-1)}{15}\times\frac{(i-2)}{14}\times\frac{1}{13}$

IDK just something feels wrong. Any help?

Thanks