Discrete Math: Unit 2 Review Combinatorics

Calculate the following.

• 990

• 165

• 33

• 575

The board of directors of a corporation has 12 members. How many ways can one choose a committee of 3-members (President, Vice President, and Secretary)?

• 1,230

• 220

• 1,320

• 760

There are 119 Division 1A college football teams. How many Top 25 rankings are possible?

• 119!

• $\frac{119!}{94!}$

• $\frac{119!}{94!\times25!}$

• 25!

Calculate the following.

• 920

• 720

• 120

• 60

If you have 6 shirts, 5 pants, and 3 hats, how many different shirt/pants/hat outfits are possible?

• 14

• 18

• 30

• 90

A restaurant offers 7 sides, 4 entrees, and 2 desserts. How may different lunch specials are possible if you have to get 1 of each?

• 24

• 48

• 56

• 96

A restaurant offers 7 sides, 4 entrees, and 2 desserts. How many different lunches could you order if you wanted an entree and either a dessert or side to eat?

• 24

• 36

• 48

• 56

A 5-question quiz has answer choices A, B, C, D, and E. How many different ways could students write answers to the quiz?

• 3,125

• 625

• 125

• 1

A 5-question quiz has answer choices A, B, C, D, and E. If the students knew that each answer was only used once, how many different ways could they answer the quiz?

• 3,125

• 625

• 120

• 1

A password using numbers and letters must be 7 characters long and it is not case sensitive.

How many password are possible with no restrictions?

• ₃₆P₇

• ₃₆C₇

• 7!

• 36⁷