## Practice Problems

If you need some more help, you may want to review the Permutations section again.

### Problems With Solutions

1. How many different ways can you arrange the letters of the alphabet?

2. How many different ways can you arrange the letters of the word "VISITING"? How many of these arrangements have all three I's next to each other?

3. Determine how many different five-digit numbers may be made from the digits 4, 3, 7, 8, and 9. How many of these numbers are even? How many are odd? How many start with the number 7?

4. Josh has seven cookbooks on a shelf. Four of them deal with Italian food, and three of them are concerned with Greek food. How many ways can he arrange the cookbooks...

• if there are no restrictions?
• if the different food styles must alternate?
• if all the Greek cookbooks must be next to each other?
• if all the Greek cookbooks must be next to each other, and all the Italian cookbooks must be next to each other?

5. Marion is standing on the corner of Madison Street and Commonwealth Avenue. How many different routes may she take when driving to the supermarket? (assume that she takes the shortest route)

1. Which state has more arrangements for the letters of its name, MISSISSIPPI or PENNSYLVANIA? [Solution]

2. How many ways can you arrange the letters x, x, x, x, y, y, y, z, z in a row? [Solution]

How many of these arrangements start with x and end with y? [Solution]

3. When playing the card game Bridge, each player recieves 13 cards. If you recieve all hearts, how many different ways can you arrange them...
• if there are no restrictions? [Solution]
• if the 2 of hearts must be next to the Ace of hearts? [Solution]
• if the 2 of hearts must not be next to the Ace of hearts? [Solution]
• if all the odd cards must be next to each other and all of the face cards must be next to each other? [Solution]

4. Find the number of ways in which 4 boys and 4 girls can be seated in a row of 8 seats if they sit alternately. [Solution]

5. There is a boy named Micah and a girl named Loretta in problem number 4, and they cannot be seated next to each other or else they will fight. How many permutations are there now? [Solution]

6. Heather is on her way to her music lesson which is at the Music Shop. However, she cannot travel down Lane Ave., because it is closed for construction. How many different ways can she get to the Music Shop, assuming that she always takes the shortest route? [Solution]

After completing the pratice problems, move on to the Combinations page!

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