# Lesson Worksheet: Counting Using Permutations Mathematics • 12th Grade

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

Q1:

Let and . Determine the value of , where is the number of elements in .

Q2:

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

Q3:

How many unique anagrams are there of the word ERROR?

Q4:

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?

• A
• B
• C
• D

Q5:

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.

Q6:

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

• ATrue
• BFalse

Q7:

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.

Q8:

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

Q9:

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?

Q10:

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