1. Show the probability distribution of the following using two different ways: [6]

Twenty out of 30 people at a party are

non-smokers. The random variable is

the number of smokers in a selection of

8 partiers.

Alexander is creating a 10-character password that consists of numbers and letters. He is not allowed to have repeated characters, but lower case letters and upper-case letters are allowed (i.e. "a" and "A" will be considered different characters).

1. How many different passwords can he create if "a" and "A" must be a part of the password.

How many different passwords can he create if there must be at least 8 digits in the password?