Intro to Permutations & Combinations

Permutation, combination, or neither?
The batting order for seven players on a 12 person team.

• combination
• permutation
• neither

Erik gets to choose from five cake flavors, seven icing flavors, and three topping flavors. If he can only choose one of each flavor,  how many cakes are possible?

• 35
• 573
• 21
• 105

How many ways can you choose a manager and assistant from a 9-person task force?

• 81
• 18
• 72

Find the number of possibilities:

A team of 17 softball players needs to choose three players to refill the water cooler.

• 272

• 4080

• 680

There are 11 runners in a race. If the first three runners all receive a different prize, in how many ways can these prizes be awarded?

[There are no ties, and at least three runners finish the race.]

• 33

• 1,331

• 990

• 177,147

A large family has 8 children. If they all line up in a row for a photo, in how many ways can this photo be taken, respective of order?

• 8

• 64

• 40,320

• 16,777,216

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

• 45
• 362,880
• 90

How would you solve?

From the 20 DVD's you purchased this past year, you plan to take five with you on vacation. How many different sets of five DVD's can you take?

• Permutation

• Counting Principles

• Factorial

• Combination

A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?

• 16

• 8

• 64

• 512

What is 4! called?

• Fabulous Four

• Final Four

• Four Factorial

• Four Factored