# Worksheet: Properties of Permutations

In this worksheet, we will learn how to use the properties of permutations to simplify expressions and solve equations.

**Q1: **

Find the value of given that .

**Q2: **

If , find .

**Q3: **

If , find the value of .

**Q4: **

Find the solution set of the equation .

- A
- B
- C
- D

**Q5: **

Find the smallest value of satisfying the inequality .

**Q6: **

If the middle factor in the expansion of is 69, find the value of .

**Q7: **

Find the value of satisfying the equation .

**Q8: **

Evaluate .

**Q9: **

Find the value of such that .

**Q10: **

Evaluate given that .

**Q11: **

If and , find .

**Q12: **

If and , find the value of .

**Q13: **

If and , find .

**Q14: **

Given that , determine the value of .

**Q15: **

If , find .

**Q16: **

Find such that .

**Q17: **

If , find the value of .

**Q18: **

If and , find and .

- A,
- B,
- C,
- D,

**Q19: **

Find the value of such that .

**Q20: **

If , find .

**Q21: **

Find the smallest value of which satisfies the inequality .

**Q22: **

Evaluate .

**Q23: **

Evaluate .

**Q24: **

Find the value of given that .

**Q25: **

Find the value of given that .