Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:

(a) Compute the probability that 10 people have different birthdays.

(b) The complement of "10 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 10 share the same birthday.