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 𝑛 given that 𝑃=3!.

Q2:

If 𝑃=1,320, find 𝑃.

Q3:

If 34𝑛!=720, find the value of 𝑃 .

Q4:

Find the solution set of the equation 240𝑃=𝑃.

  • A{19}
  • B{12}
  • C{24}
  • D{38}

Q5:

Find the smallest value of 𝑛 satisfying the inequality 𝑃>𝑃.

Q6:

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

Q7:

Find the value of 𝑥 satisfying the equation 𝑃5𝑥𝑃=0.

Q8:

Evaluate 𝑃×2!.

Q9:

Find the value of 𝑚 such that 𝑃=4,080.

Q10:

Evaluate (𝑟+2)! given that 𝑃=336.

Q11:

If 𝑃=120 and 𝑟!=24, find 𝑃.

Q12:

If 𝑃=720 and 𝑟!=120, find the value of (9𝑟7𝑛)!.

Q13:

If 𝑃=360 and (2𝑥+𝑦)!=5,040, find 𝑃.

Q14:

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

Q15:

If 𝑃=23(𝑃), find 𝑛.

Q16:

Find 𝑚 such that 𝑃=𝑃.

Q17:

If 𝑃=34×𝑃, find the value of (𝑟6)! .

Q18:

If 𝑃=35,904 and 𝑛+𝑚=60, find 𝑚 and 𝑛.

  • A𝑚=47, 𝑛=13
  • B𝑛=34, 𝑚=94
  • C𝑛=94, 𝑚=34
  • D𝑛=47, 𝑚=13

Q19:

Find the value of 𝑛 such that 𝑃=32,736.

Q20:

If (𝑛+1)!(𝑛1)!=72, find 𝑃+𝑃+𝑃.

Q21:

Find the smallest value of 𝑛 which satisfies the inequality 𝑃>𝑃.

Q22:

Evaluate 𝑃+𝑃+𝑃.

Q23:

Evaluate 𝑃𝑃.

Q24:

Find the value of 𝑛 given that 𝑃=24.

Q25:

Find the value of 𝑦 given that 𝑃=2,184.

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