Factorials and Permutations

Determine the number of 4-letter arrangements that can be made using the word RHOMBUS.

• 5040

• 35

• 28

• 840

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• 324

• 4,896

• 816

• 54

How many ways can you arrange 7 books on a shelf?

• 7

• 49

• 343

• 5,040

The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?

• 720

• 120

• 10!

What is the value of 5!

• 25

• 15

• 120

• 720

9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

• 45

• 362,880

• 90

7 * 6 * 5 * 4 * 3 * 2 * 1

• 42

• 28

• 5,040

Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• 1
• 3628800
• 100
• 1814400

How many ways can you listen to 3 songs from a CD that has 12 selections?

• 1320

• 33

• 36

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

• 23

• 840

• 42

• 3,628,800