FCP and Permutation

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!

Describe the Type of Problem:

In a town election, there are 10 people running for Trustee, Plow-Man, and Landscaper

• Combination

• Permutation

• Fundamental Counting Principle

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

• 3,628,800

• 100

• 1,814,400

Simply the expression: 9P4

• 36

• 120

• 35

• 3024

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

• 23

• 840

• 42

• 3,628,800

Simplify the expressions 6P5

• 1

• 30

• 720

• 6

Calculate the following:

₁₂P₅

Mathematical Equivalence

ON

How many ways can 8 runners finish in the top 3 places where the prizes for 1^st, 2^nd, and 3^rd are all different and matter?

Mathematical Equivalence

ON

Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?  

• 5,100,480

• 0

• 42,504

• 5.17 x 10²¹