A California license plate has 11​ digit followed by 33​ letters followed by 33​ more digits. How many California license plates are possible? Repeated digits and letters are allowed.

1. A California license plate has 11​ digit followed by 33​ letters followed by 33​ more digits. How many California license plates are possible? Repeated digits and letters are allowed.
2. A website instructs users to create a password using 1010​ alphanumeric characters (letters or digits). Capitalization doesn’t matter. How many such passwords are possible that end in the letter Z?
3. DNA is made of codons, which are sequences of three of the following molecules: Guanine (G), Adenosine (A), Cytosine (C), and Thymine (T). Repetitions are normal. How many different codons are possible that start with Guanine?
4. Using a standard deck of 5252​ cards, how many 55​-card hands contain 33kings and 22 queens?
5. Using a standard deck of 5252​ cards, how many 66​-card hands contain all hearts?
6. In the Mucho Millions lottery, players choose 66​ different numbers between 11​ and 5050​ and 11​ number between 11​ and 2929​​. The order of the numbers does not matter. How many different lottery tickets are possible?
7. Using a standard deck of 5252​ cards, what is the probability that a randomly dealt 33​-card hand contains all hearts?
8. Using a standard deck of 5252​ cards, what is the probability that a randomly dealt 55​-card hand contains 33​ kings and 22​ cards that aren’t kings?
9. In the Lotsa Millions Lottery, players pick 66​​ numbers from between 11​ and 4444​. The order of the numbers doesn’t matter and numbers cannot be repeated. What is the probability that a randomly selected ticket will match exactly ​22​ out of the 66​​ winning numbers?

10. A game costs \$2.00$2.00​ to play. In the game, the player picks a card at random from a standard deck of cards. If the card is a face card, the player receives \$6.00$6.00​, if the card is not a face card, the player receives nothing.

What is the expected value for the player? Round your answer to the nearest cent.

11. In a certain game, a player picks a card at random from a standard deck of cards. If the card is a heart, the player wins \$25.00$25.00. Otherwise, the player loses \$5.00$5.00.

What is the expected value of this game for the player?

12. An American roulette wheel has 3838​ spaces and if a player wins they keep their bet. Suppose that a \$3.00$3.00bet on a single space wins \$105.00$105.00 if the space is landed on and, otherwise, the player wins nothing. What is the expected value of this bet from the casino’s standpoint? Round your answer to the nearest cent.
13. As a fundraiser, the local charity is raffling off a prize worth \$500.00$500.00. They plan to sell 700700tickets at a cost of \$1.00$1.00

What is the expected value per ticket from the standpoint of the charity? Round your answer to the nearest cent.

14. Suppose that the probability of a certain 2222​-year-old person dying within a year is 0017530.001753. They are offered a \$225{,}000.00$225,000.00life insurance policy for that year and the policy comes at a one-time cost of \$275.00$275.00.

What is the expected value from the standpoint of the insurance company? Round your answer to the nearest cent.