Worksheet: Properties of Permutations

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

Q1:

Evaluate 𝑃 .

Q2:

Evaluate 𝑃 + 𝑃 .

Q3:

Evaluate 𝑃 × 𝑃 .

Q4:

Evaluate 𝑃 𝑃 .

Q5:

Find the value of 𝑛 given that 𝑛 1 0 2 𝑃 = 3 .

Q6:

If 𝑃 = 1 , 3 2 0 , find 𝑃 .

Q7:

If 3 4 𝑛 ! = 7 2 0 , find the value of 𝑃 .

Q8:

Find the solution set of the equation 2 4 0 𝑃 = 𝑃 𝑥 + 2 2 𝑥 + 4 4 .

  • A { 2 4 }
  • B { 1 9 }
  • C { 3 8 }
  • D { 1 2 }

Q9:

Find the smallest value of 𝑛 satisfying the inequality 𝑛 2 5 𝑛 2 4 𝑃 > 𝑃 .

Q10:

If the middle factor in the expansion of 𝑛 2 3 𝑃 is 69, find the value of 𝑛 .

Q11:

Find the value of 𝑥 satisfying the equation 1 0 7 𝑥 1 0 7 𝑥 1 𝑃 5 𝑥 𝑃 = 0 .

Q12:

Find the value of the permutation for 𝑛 = 6 and 𝑟 = 2 .

Q13:

Evaluate 𝑃 × 2 ! .

Q14:

Find the value of 𝑚 such that 𝑃 = 4 , 0 8 0 .

Q15:

Evaluate ( 𝑟 + 2 ) ! given that 𝑃 = 3 3 6 .

Q16:

If 𝑃 = 1 2 0 and 𝑟 ! = 2 4 , find 𝑃 .

Q17:

If 𝑃 = 7 2 0 and 𝑟 ! = 1 2 0 , find the value of ( 9 𝑟 7 𝑛 ) ! .

Q18:

If 𝑥 + 𝑦 4 𝑃 = 3 6 0 and ( 2 𝑥 + 𝑦 ) ! = 5 0 4 0 , find 𝑦 𝑥 𝑃 .

Q19:

Given that 𝑛 4 𝑛 1 3 𝑃 = 8 × 𝑃 , determine the value of 𝑛 .

Q20:

If 𝑛 1 5 𝑛 1 1 4 𝑃 = 2 3 𝑃 , find 𝑛 .

Q21:

Find 𝑚 such that 𝑃 = 𝑃 .

Q22:

If 𝑃 = 3 4 × 𝑃 , find the value of ( 𝑟 6 ) ! .

Q23:

If 𝑃 = 3 5 , 9 0 4 and 𝑛 + 𝑚 = 6 0 , find 𝑚 and 𝑛 .

  • A 𝑛 = 9 4 , 𝑚 = 3 4
  • B 𝑚 = 4 7 , 𝑛 = 1 3
  • C 𝑛 = 3 4 , 𝑚 = 9 4
  • D 𝑛 = 4 7 , 𝑚 = 1 3

Q24:

Find the value of 𝑛 such that 𝑛 3 𝑃 = 3 2 7 3 6 .

Q25:

If ( 𝑛 + 1 ) ! ( 𝑛 1 ) ! = 7 2 , find 𝑃 + 𝑃 + 𝑃 .

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