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:

Find the value of

Q4:

Evaluate 2 ! 7 ! .

  • A5
  • B 2,520
  • C 1 9
  • D 1 2 , 5 2 0
  • E9

Q5:

Simplify the expression 6 ! 4 ! 2 7 ! 2 8 ! . Give your answer as a fraction.

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

Q6:

Find the value of 𝑛 such that 𝑛 ! = 7 2 0 .

Q7:

Find the solution set of ( 𝑛 2 6 ) ! = 0 ! .

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

Q8:

Find the value of 𝑛 such that 𝑛 ( 8 𝑛 1 ) ! = 5 , 0 4 0 .

Q9:

Find the solution set of 𝑛 + 1 𝑛 1 = 3 0 .

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

Q10:

Find the value of 𝑛 that satisfies the relation ( 𝑛 2 8 ) ! 6 ! = 7 ! 𝑛 2 7 .

Q11:

Find the solution set of 1 ( 𝑛 + 7 ) ! + 1 ( 𝑛 + 8 ) ! = 2 5 6 ( 𝑛 + 9 ) ! .

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

Q12:

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

Q13:

Evaluate 7 ! + 6 ! + 5 ! .

Q14:

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

Q15:

Simplify the expression 2 8 ! 2 7 ! 4 6 ! 4 7 ! , giving your answer as a fraction.

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

Q16:

Evaluate 1 ! .

Q17:

If 𝑃 𝑃 = 1 7 1 8 , find 𝑛 ! .

Q18:

Given 𝑃 = 6 , 7 2 0 , evaluate the expression ( 𝑥 7 ) ! .

Q19:

Given that 𝑃 = 5 0 4 and 𝑟 ! = 6 , find the values of 𝑛 and 𝑟 .

  • A10, 3
  • B9, 4
  • C10, 4
  • D9, 3

Q20:

Evaluate 6 ! 5 ! .

  • A1
  • B 1 6
  • C 1 1 1
  • D6
  • E11

Q21:

If 2 5 × 𝑃 ( 𝑥 ) ! = 2 5 ! , find the value of ( 𝑥 1 7 ) ! .

Q22:

Find 𝑧 such that 𝑧 ! = 1 2 0 .

Q23:

If 𝑃 = 6 0 0 and ( 𝑥 𝑦 ) ! = 3 6 2 , 8 8 0 , find ( 2 𝑥 3 𝑦 ) ! .

Q24:

If 𝑃 𝑛 ! ( 𝑛 3 ) ! = 7 , find 𝑛 .

Q25:

If 𝑃 𝑃 = 1 4 5 , find ( 𝑛 1 ) ! .

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