Suppose there are 6 people in a room.

This question has two parts:

(a) What is the probability that there is a shared birthday among them, i.e. that there is a pair of people who have the same birthday? Write your answer as a mathematical expression that shows your understanding (not as a single number in decimal form).

(b) If you are one of the 6 people, what is the probability that no one has the same birthday as you? Write your answer as a mathematical expression that shows your understanding (not as a single number in decimal form).