How many nine card hands are possible?

1.Dana wants to buy a new care. She is trying to choose between a Chevy, Ford, Mazda or a Honda. Each vehicle can come in one of six different colors: black, green, blue, red, silver, or brown. How many different combinations of vehicle and color does Dana have to choose from?
2. There are three different color cars parked along the side of the road, a blue car, a red car, and a green car. How many different combinations are there for the order in which these cars are parked?
3. Forty-three drivers compete in NASCAR’s Daytona 500 race every year. How many different combinations are there for the first three drivers to cross the finish line?
4.Tom and Jen decide to rent a movie. Jen wants to rent a comedy, but Tom wants to rent an action movie, so instead they decide to each rent their own movie. The rental kiosk has 16 comedies, 10 action movies, and 14 dramas. How many different combinations of two movies can they rent if they both get the type of movie they want?
5. A card game using 36 unique cards: four suits (diamonds, hearts, clubs and spades) with cards numbered 1 to 9 in each suit. A hand is a collection of nine cards, which can be sorted however the player chooses. How many nine card hands are possible?
1. A zip code contains 5 digits. How many different zip codes can be made with the digits 0–9 if no digit is used more than once and the first digit is not 0?
2. In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?
3. A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
4. How many different ways can 3 students line up to purchase a new textbook reader?
5. In one game, a code made using different colors is created by one player (the codemaker), and the player (the codebreaker) tries to guess the code. The codemaker gives hints about whether the colors are correct and in the right position.
The possible colors are Blue, Yellow, White, Red, Orange and Green. How many 4-color codes can be made if the colors cannot be repeated?
In your responses, you must provide the solution and the reasoning behind your solution. Explain your work.

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