# Worksheet: Counting Using Permutations

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

**Q2: **

Which of the following represents the number of ways in which 2 boys can sit in a row of 24 seats?

- A
- B
- C
- D

**Q3: **

Which of the following represents the number of ways in which the letters of the word โmelonsโ can be rearranged?

- A
- B
- C
- D

**Q4: **

Which of the following represents the number of ways we can form a password of length 13 characters using different English letters.

- A
- B
- C
- D

**Q5: **

Which of the following represents the number of ways in which a president and a vice president can be elected from a committee of 17 members?

- A
- B
- C
- D

**Q6: **

In how many ways can a three-digit number, with no repeated digits, be formed using the numbers 2, 9, and 8?

**Q7: **

Which of the following represents the number of ways a 4-digit number can be formed from 5 digits, given that each digit can NOT be used more than once?

- A
- B
- C
- D

**Q9: **

Michel, Kayla, and ChiWei are playing a game, where one of them needs to be a sheriff and one needs to be an outlaw. They write each of their names on a piece of paper and place them in a bowl. If two names are picked at random where the first will be a sheriff and the second will be an outlaw how many different combinations are there?

**Q10: **

A company labels their products with codes that start with three English letters followed by eight 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

**Q11: **

A mall has 6
doors that are both entrances and exits.
Which of the following represents the number of ways you can enter and leave the mall if you do
**not** use the same door twice?

- A
- B
- C
- D

**Q12: **

Let and , where . Which of the following represents the number of elements in ?

- A
- B
- C
- D

**Q13: **

Find the solution set of .

- A
- B
- C
- D

**Q14: **

Evaluate .

- A
- B
- C
- D

**Q15: **

If and , find .

**Q16: **

Given that six times the number of permutations of three elements taken from a set of elements equals eight times the number of permutations of three elements taken from a set of elements, find the value of .

**Q17: **

Calculate .

**Q18: **

Calculate .

- A
- B
- C
- D

**Q19: **

By using to find the value of , evaluate the expression .

**Q20: **

Calculate .

- A
- B
- C
- D

**Q21: **

If , find .

**Q22: **

If and , find .

**Q23: **

Evaluate the expression , given that .