Worksheet: Factorials

In this worksheet, we will practice finding the factorial of a known number and finding an unknown variable in an equation has factorial.

Q1:

Evaluate 4!.

Q2:

Evaluate 6!4!2!.

Q3:

Evaluate 2!3!.

Q4:

Evaluate 2!7!.

  • A9
  • B2,520
  • C 1 2 , 5 2 0
  • D5
  • E 1 9

Q5:

Simplify the expression 6!4!27!28!. Give your answer as a fraction.

  • A 2 9 2 7
  • B 8 3 9 2 8
  • C 8 4 1 2 8
  • D 2 8 8 4 1
  • E 2 8 8 3 9

Q6:

Find the value of 𝑛 such that 𝑛!=720.

Q7:

Find the solution set of (𝑛26)!=0!.

  • A { 2 6 , 2 7 }
  • B { 0 , 2 7 }
  • C { 2 7 }
  • D { 2 6 }
  • E { 0 , 1 }

Q8:

Find the value of 𝑛 such that 𝑛(8𝑛1)!=5,040.

Q9:

Find the solution set of (𝑛+1)!(𝑛1)!=30.

  • A { 9 }
  • B { 5 }
  • C { 6 }
  • D { 2 0 }

Q10:

Find the value of 𝑛 that satisfies the relation (𝑛28)!6!=7!𝑛27.

Q11:

Find the solution set of 1(𝑛+7)!+1(𝑛+8)!=256(𝑛+9)!.

  • A { 9 }
  • B { 2 5 }
  • C { 8 }
  • D { 7 }

Q12:

If 𝑃=9(𝑃), evaluate the expression (𝑑+1)!(𝑑+2)!+𝑑!(𝑑+1)!+(𝑑2)!(𝑑1)!. Give your answer as a decimal.

Q13:

Evaluate 7!+6!+5!.

Q14:

Given 𝑃=4(𝑃), find (𝑥+1)!(𝑥+2)!+𝑥!(𝑥+1)!+(𝑥2)!(𝑥1)!.

Q15:

Simplify the expression 28!27!46!47!, giving your answer as a fraction.

  • A 2 7 4 6
  • B 1 , 3 1 7 4 7
  • C 4 7 1 , 3 1 7
  • D 1 , 3 1 5 4 7
  • E 4 7 1 , 3 1 5

Q16:

Evaluate 1!.

Q17:

If 𝑃𝑃=1718, find 𝑛!.

Q18:

Given 𝑃=6,720, evaluate the expression (𝑥7)!.

Q19:

Given that 𝑃=504 and 𝑟!=6, find the values of 𝑛 and 𝑟.

  • A9, 3
  • B10, 3
  • C9, 4
  • D10, 4

Q20:

Evaluate 6!5!.

  • A 1 6
  • B 1 1 1
  • C6
  • D1
  • E11

Q21:

If 25×𝑃(𝑥)!=25!, find the value of (𝑥17)! .

Q22:

Find 𝑧 such that 𝑧!=120.

Q23:

If 𝑃=600 and (𝑥𝑦)!=362,880, find (2𝑥3𝑦)! .

Q24:

If 𝑃𝑛!(𝑛3)!=7, find 𝑛.

Q25:

If 𝑃𝑃=145, find (𝑛1)!.

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