1. In how many different ways can you arrange the letters in the word, "penned?"

2. I have a password consisting of 6 digits (0 - 9). What is the probability that you can guess the password in a single try if...

a. there are no repeated digits.

b. repetition is allowed

3. there is a 1/3,000,000,000 chance of winning a lottery on a single ticket.

a. If I buy one ticket each week for 2,100 weeks, what is the probability that I will win at least once?

b. If the tickets cost $10 each, how much money will I spend buying one ticket each week for 2,100 weeks?

4. A sample of the patients seen by an Urgent Care in one day are: 11 children with influenza A, 5 adults with influenza A, 3 children with influenza B and 12 adults with influenza B.

a. If one patient is randomly selected from the sample, what is the probability that the person has influenza A given that the patient is a child?

b. If one patient is randomly selected from the sample, what is the probability that the person is a child given that the patient has influenza A?