Lesson Worksheet: Counting Using Permutations Mathematics • 12th Grade

In this worksheet, we will learn how to use permutations to solve counting problems.


Let 𝑋={𝑥𝑥,7𝑥16} and 𝑌={(𝑎,𝑏)𝑎,𝑏𝑋,𝑎𝑏}. Determine the value of 𝑛(𝑌), where 𝑛(𝑌) is the number of elements in 𝑌.


Determine the number of different ways for 4 players to sit on 11 seats in one row.


How many unique anagrams are there of the word ERROR?


A company labels their products with codes that start with 3 English letters followed by 8 non-zero digits. Which of the following represents the number of codes that can be created with no repetition of any letter or digit?

  • A𝑃+𝑃
  • B𝑃+𝑃
  • C𝑃×𝑃
  • D𝑃×𝑃


Find the number of ways we can pick 2 milk chocolate bars and 2 dark chocolate bars from a box of 10 milk chocolate bars and 8 dark chocolate bars, considering that the elements are distinct and the arrangement is without replacement, and the order of selection matters.


True or False: In a flower shop, there are 40,320 ways to arrange 8 flowers in a circle.

  • ATrue
  • BFalse


In a football league, a team plays every other team twice. If there are 14 teams in the league, determine the total number of matches to be played.


In how many ways can we form a number with 2 or more distinct digits, using the elements of the set {3,4,8}?


We have four number cards that are numbered 3, 4, 5, and 6. How many unique numbers can we form using at least 1 of the cards?


In how many ways can we arrange 2 different colored balls on a shelf that can hold 20 balls?

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