Birthday Collision Probability and Exponential Approximation

Fifty people are in a room. Each birthday is independent and uniform on $\{1, 2, \ldots, 365\}$.

(a) Write the exact probability that at least two share a birthday.

(b) Derive a useful upper bound on $P(\text{all distinct})$ using the inequality $1-x \le e^{-x}$ and simplify. How does the approximation compare to the exact value?