Question 1. (7 points) Counting Problems a) How many three-digit numbers less than 600 can be made using the digits 8, 6, 4, and 2? Each of these digits may be used more than once (e.g., 444). b) In one state, automobile license plates must: start with two digits (0 to 9), but the first cannot be a zero. followed by two upper-case letters (A to Z), followed by a string of two to four digits (leading zeros are allowed). How many different license plates are possible? Question 2. (8 points) A survey of 150 college students reveals that 83 own automobiles, 97 own bikes, 28 own motorcycles, 53 own a car and a bike, 14 own a car and a motorcycle, 7 own a bike and a motor- cycle, and 2 own all three. a) How many students own a bike and nothing else? b) How many students do not own any of the three? Question 3. (6 points) How many people must be in a group in order to guarantee that three people in th group have the same birthday? (Don't forget about leap year) Question 4. (6 points) Consider rolling a pair of fair, six-sided dice. a) What is the probability of getting a 7 or 11? b) What is the probability of getting doubles (the same number on each die)? c) What is the probability of getting a sum on the dice of 4 or less