Read the following problems and compute the number of possibilities.
Q1. How many different 5--card poker hands containing only Diamonds are possible?
Q2. The North American Numbering Plan (NANP) has established a special protocol for how area codes are numbered. The first digit of an area code can be any of the numbers 2--9, while the second and third digit can be any of the numbers 0--9. How many area codes can be generated in this way?
Q3. A certain state uses the following rules to create license plates: Two letters followed by three digits. How many possible license plates can be created using those rules?
Q4. A particular level of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order. There are 3 red towers, 5 grey towers, and 2 green towers to choose from for this level. How many different arrangements of towers are possible?
Q5. A campus coffee shop offers 15 types of hot beverage (coffee, tea, etc.), 8 varieties of sandwich, 12 types of cold beverage (soda, energy drinks, juice) and 11 different types of bagel. How many different meals could be purchased if you wanted either a hot beverage and a bagel, or a cold beverage and a sandwich?
Q6. A puzzle requires you to find a correct three--color code using only three colors: Red, Blue, and Yellow. Any color may be placed in any or all of the three positions. How many possible combinations are there?
Q7. A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information. How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants?
Q8. In the World Series, the American League Champion plays the National League Champion. How many World Series match--ups are possible if there are 14 teams in the American League and 16 teams in the National League?
Q9. Characters in a Roman--style game are assigned a name in the Tria Nomina style: which is Praenomina (first name) Nomen (middle name) Cognomen (last name). There are only about 17 common Praenomina, but 130 Nomen and 193 common Cognomen. How many unique character names can be generated?
Q10. How many different ways can you arrange 15 billiard balls in a triangular rack?