Introduction to Counting & Probability links & errata

Below are some of the links that are referenced in the book Introduction to Counting & Probability. (Note: Art of Problem Solving is not responsible for the content on any external site.)

How to Use This Book

Chapter 1

Chapter 4

Chapter 13

Unfortunately, the book is not perfect. Here is a list of the known errors. If you know of an error not on this list, we would appreciate a short email to books@artofproblemsolving.com describing the error.

Text:

• Intro, page iv, last line before "Hints": "...you are on your way..."

Solutions:

• Chapter 1, Problem 1.3.4, page 2: "rollover" should be "roll over" in a few places
• Chapter 2, Problem 2.31(d), page 17: "palindrome" is misspelled in one place
• Chapter 11, Problem 11.14(c), page 82: "...four of the ten slips..."

Errors listed below are errors in earlier editions that have been corrected in the current (2016) edition.

Text:

• Resources, page v: mathematics is misspelled in the first sentence.
• Chapter 1, page 5: "We can start by noting that 20³ = 8000,..."
• Chapter 2, page 30, Problem 2.3: The cases should be numbered 1 through 4.
• Chapter 2, page 36, solution to Problem 2.5: In two places the book says "3-letters words" where it should say "3-letter words".
• Chapter 2, page 47, Problem 2.31: palindromes read the same forwards and backwards.
• Chapter 3, page 54, last sentence: "This may seem like..."
• Chapter 3, page 57, exercise 3.3.5: icosahedron is misspelled.
• Chapter 4, page 71, last paragraph of solution to 4.6: "..., where the two players involved in the match is a "committee".
• Chapter 5, page 92, first bullet point in Summary: "...and b total steps in another direction,..."
• Chapter 5, page 92, third bullet point in Summary: "When solving a counting problem,..." (no "s" after "problem").
• Chapter 5, page 94, Problem 5.20: "In this problem, people and desks..." (no "that").
• Chapter 6, page 103, first sentence: "...path from A to B would consist of 5 steps..."
• Chapter 6, page 103, parenthetical note about halfway down the page: "...in other words, we could start at A and work...".
• Chapter 8, page 126, last sentence of 2nd paragraph: "Thus there are..."
• Chapter 8, page 137, solution to Problem 8.14: Says "The probability that that the first marble is blue..."; should only be one "that".
• Chapter 8, page 138, Problem 8.16 (and again on page 139, and sadly in a couple of other places too): Mandelbrot is misspelled.
• Chapter 10, page 154, Problem 10.2: Should be "...|x-1| ≤ ½" (to match the solution on page 155).
• Chapter 13, page 205, first item in Summary: Should be "... n pieces of candy to k kids" (the book has the n and the k reversed).
• Chapter 13, page 206, Problem 13.7(b): the intended interpretation is that "some" might also include "none". So 0 students choosing to not vote should be included in the possibilities. A better wording would be "(b) if some student(s) possibly decide not to vote?"
• Chapter 15, page 225, first sentence: Should say "...better geometrician than I!"

Solutions:

• Chapter 1, Problem 1.19, page 4: The second sentence should be "...divisible by 7 is...divide this list by 7, we get...".
• Chapter 3, Problem 3.2.3(i), page 21: The final calculation should be 5! / (2! x 2!) = 30.
• Chapter 5, Problem 5.4.2(c), page 35, 3rd paragraph: "There are 3!=6 ways to arrange..."
• Chapter 5, Problem 5.16(b), page 38: The total should be 1+4+3+6 = 14.
• Chapter 6, Problem 6.10, page 42: The word objects is misspelled.
• Chapter 6, Problem 6.15(b), page 43: There's a typesetting error in Case 3; it should be C(4,2) x C(4,2) = 36.
• Chapter 7, Problem 7.2.2(b): The word card is misspelled.
• Chapter 7, Problem 7.17: "...So an even product can occur in 36 - 9 **=** 27 ways,..."
• Chapter 8, Problem 8.4.2(a), page 56: "...each die can be odd or even".
• Chapter 8, Problem 8.19, page 60: Should be (1/2)⁶.
• Chapter 8, Problem 8.28, page 62: The count in case 1 is 1085, but in the final paragaph, the number is incorrectly reported as 1058. The final paragraph should read: "So there are 1085+2268=3353 successful ways...", and the final answer should be 3353/7280 = 479/1040.
• Chapter 9, Problem 9.17, page 68: The third term in the infinite series at the end of Case 3a should be (2/3 x 1/3 x 2/3 x 1/3 x 1/3) (to match what is in the previous sentence).
• Chapter 10, Problem 10.3.4, page 73: The diagram is incorrect. The region above the line y=x should be shaded.
• Chapter 11, Problem 11.3.6, page 79: The answer, although correct, is not in lowest terms; it should be 13/3.
• Chapter 11, Problem 11.16, page 83: The final answer is 9/2.
• Chapter 12, Problem 12.5.2, page 87: The last term on the left side of the last equation should be C(2n,2n), not C(2n,n).
• Chapter 14, Problem 14.5.4, page 102, first line of equation: last term should be (-3)C(19,19).