This document contains 13 examples of permutations and combinations problems from a Mathematics 4 class. It provides example problems involving passcode combinations, palindromes, paths on a grid, lottery number selection, triangles in an octagon, quiz answers, multiple choice exams, hamburger toppings, NBA championship series outcomes, poker hands, and donut flavors. The document is intended to illustrate different applications of permutations and combinations in mathematics.

1. Examples on Permutations and Combinations
Mathematics 4
February 23, 2012
Mathematics 4
Examples on Permutations and Combinations

2. Example
A stalker classmate observed that her crush’s smartphone has
fingerprint smudges corresponding to the numbers 2,4,7, and 9 on
the passcode entry screen. She correctly figures out that her
crush’s passcode must be using those four digits. What is the
largest possible number of trials that she needs to take to access
the contents of the smartphone?
Mathematics 4
Examples on Permutations and Combinations

3. Example
How many 7 digit numerical palindromes are there? (Example:
34543)
Mathematics 4
Examples on Permutations and Combinations

4. Example
Given the grid below, how many paths from A to B are possible if
moves are restricted to the right or up?
Mathematics 4
Examples on Permutations and Combinations

5. Example
How many ways can a player select six numbers in the Lotto 6/42
game?
Mathematics 4
Examples on Permutations and Combinations

6. Example
How many different triangles can be formed by connecting any 3
points in the vertices of a regular octagon?
Mathematics 4
Examples on Permutations and Combinations

7. Example
How many different triangles can be formed by connecting any 3
points in the vertices of a regular octagon?
Mathematics 4
Examples on Permutations and Combinations

8. Example
How many ways can a student answer 10 questions correctly in a
15 item quiz?
Mathematics 4
Examples on Permutations and Combinations

9. Example
If each test item in the quiz above is a multiple choice question
with 4 choices each, how many ways can a student answer the
exam?
Mathematics 4
Examples on Permutations and Combinations

10. Example
If each test item in the quiz above is a multiple choice question
with 4 choices each, how many ways can a student make 5
mistakes in the exam?
Mathematics 4
Examples on Permutations and Combinations

11. Example
A customer in a fast food restaurant can choose any combination
out of 7 condiments on a hamburger. How many burger sandwich
combinations can the customer make?
Mathematics 4
Examples on Permutations and Combinations

12. Example
The winner of the seven-game NBA championship series is the
team that wins four games. In how many different ways can the
series finish in seven games?
Mathematics 4
Examples on Permutations and Combinations

13. Example
A full house is a hand that consists of three cards of one
denomination and two cards of another denomination. How many
5-card hands are full houses?
Mathematics 4
Examples on Permutations and Combinations

14. Example
How many ways can we buy 12 donuts out of an unlimited supply
of 5 flavors?
Mathematics 4
Examples on Permutations and Combinations