Q: A code consists of 2 letters followed by 2 digits. How many codes are possible if letters and digits cannot be repeated?

$$26 \times 25 \times 10 \times 9$$

Question 1

A restaurant offers 7 appetizers and 11 main courses. In how many ways can a person order a two-course meal (one appetizer and one main course)?

Accepted Answer

$$7 	imes 11$$

Question 2

A popular brand of pen is available in 6 colors and 2 writing tips. How many different choices of pens do you have with this brand?

Accepted Answer

$$6 	imes 2$$

Question 3

A sales representative can take one of 3 different routes from City C to City F and any one of 7 different routes from City F to City M. How many different routes can she take from City C to City M, going through City F?

Accepted Answer

$$3 	imes 7$$

Question 4

In a different plan for area codes, the first digit could be any number from 0 through 5, the second digit was either 7 or 8, and the third digit could be any number except 5. With this plan, how many different area codes are possible?

Accepted Answer

$$6 	imes 2 	imes 9$$

Question 5

There are six performers who will perform their comedy acts this weekend at a comedy club. How many different ways are there to schedule their appearances?

Accepted Answer

$$6!$$

Question 6

There are 7 performers who will present their acts at a talent show this weekend. One of the performers insists on going last. If this performer’s request is granted, how many different ways are there to schedule the appearances?

Accepted Answer

$$6!$$

Question 7

You need to arrange five of your favorite books along a small shelf. How many different ways can you arrange the books, assuming the order of the books makes a difference to you?

Accepted Answer

$$5!$$

Question 8

A camp counselor and six campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the third seat and a camper who has a tendency to engage in food fights must sit to the counselor’s immediate right?

Accepted Answer

$$5! 	imes 6$$

Question 9

If you have 4 different shirts and 3 different pairs of pants, how many different shirt and pant outfits can you make?

Accepted Answer

$$4 	imes 3$$

Question 10

A password consists of 2 letters followed by 3 digits. If letters and digits can be repeated, how many different passwords are possible?

Accepted Answer

$$26^2$$ 	imes $$10^3$$

Question 11

How many ways can you arrange the letters in the word 'MATH'?

Accepted Answer

$$4!$$

Question 12

A committee of 3 is to be formed from 8 people. How many different committees are possible?

Accepted Answer

$$\frac{8!}{3!5!}$$

Question 13

A lock has a 3-digit code. Each digit can be any number from 0 to 9, but no digit can be repeated. How many different codes are possible?

Accepted Answer

$$10 	imes 9 	imes 8$$

Question 14

How many different ways can 4 people be seated in a row of 4 chairs if two specific people must sit next to each other?

Accepted Answer

$$2 	imes 3!$$

Question 15

A school club has 10 members. In how many ways can a president, vice president, and secretary be chosen if no person can hold more than one office?

Accepted Answer

$$10 	imes 9 	imes 8$$

Question 16

A pizza shop offers 5 toppings. How many different pizzas can be made if each pizza can have any number of toppings (including none)?

Accepted Answer

$$2^5$$

Question 17

How many ways can you select a president and a vice president from a group of 12 people, if the same person cannot hold both positions?

Accepted Answer

$$12 	imes 11$$

Question 18

A bookshelf has 8 different books. In how many ways can you select 3 books to read, if the order does not matter?

Accepted Answer

$$\frac{8!}{3!5!}$$

Question 19

A student must answer 5 out of 10 questions on a test. In how many ways can the student choose the questions?

Accepted Answer

$$\frac{10!}{5!5!}$$

Question 20

A code consists of 2 letters followed by 2 digits. How many codes are possible if letters and digits cannot be repeated?

Accepted Answer

$$26 	imes 25 	imes 10 	imes 9$$

Combinatorics and Counting Principles – Liberal Arts Math Study Guide

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