Worksheet: Properties of Combinations

In this worksheet, we will practice solving problems involving combinations.

Q1:

Find the value of 𝑥 such that 𝐶=3,060 and 𝐶=𝐶.

Q2:

Find 𝑟 given that 𝐶>1 and 𝐶>1.

Q3:

Find the value of 𝐶𝐶+𝐶𝐶+𝐶.

Q4:

If 𝐶=120, find 𝑛.

Q5:

If 𝐶=35, find 𝐶.

Q6:

If (3𝑛5)!=24, find 𝐶.

Q7:

Given that 𝐶=2𝑛, evaluate 𝐶.

Q8:

Given that 𝐶=52𝑛, determine 𝐶.

Q9:

Find the value of 𝐶 given that 𝐶=3013𝑛.

Q10:

If 𝐶=2 and 𝐶=21, find (𝑛𝑚)!.

Q11:

Which of the following inequalities is true given that 𝐶>𝐶?

  • A 𝑛 > 3 9
  • B 𝑛 = 3 9
  • C 𝑛 < 3 9

Q12:

If 𝑛!=5,040 and 𝐶=70, find 𝐶+𝐶.

Q13:

Find the value of 𝐶+𝐶+𝐶++𝐶.

Q14:

If 𝐶=𝐶, find all the possible values of 𝑟.

  • A6
  • B3
  • C3 or 9
  • D3 or 6
  • E9

Q15:

If 𝑃=5,402, and 𝐶=104, find 𝑚 and 𝑛.

  • A 𝑚 = 8 9 , 𝑛 = 1 5
  • B 𝑛 = 8 9 , 𝑚 = 1 5
  • C 𝑛 = 7 4 , 𝑚 = 1 7 8
  • D 𝑛 = 1 7 8 , 𝑚 = 7 4

Q16:

Given that 𝐶𝐶𝐶=21515, determine 𝑛 and 𝑟.

  • A 𝑛 = 1 2 , 𝑟 = 1 4
  • B 𝑛 = 1 2 , 𝑟 = 3
  • C 𝑛 = 1 2 , 𝑟 = 2
  • D 𝑛 = 1 3 , 𝑟 = 2
  • E 𝑛 = 1 5 , 𝑟 = 2

Q17:

Given that 𝑃𝐶=20! and 𝐶𝐶=519, find 𝑛 and 𝑟.

  • A 𝑛 = 2 2 , 𝑟 = 1 9
  • B 𝑛 = 2 2 , 𝑟 = 5
  • C 𝑛 = 2 3 , 𝑟 = 1 9
  • D 𝑛 = 2 5 , 𝑟 = 2 2

Q18:

Which of the following is equal to 𝐶?

  • A 𝑃 × 5 !
  • B 𝑃 × 5
  • C 𝑃 5 !
  • D 𝑃 5

Q19:

Determine the value of 𝐶𝐶 without using a calculator.

  • A 7 3 4
  • B 4 3
  • C 7 3
  • D 5 2
  • E 3 4 7

Q20:

Find 𝑥 and 𝑦, such that 𝐶=38×𝐶 and 𝐶=𝐶.

  • A 𝑥 = 9 , 𝑦 = 2
  • B 𝑥 = 4 , 𝑦 = 2
  • C 𝑥 = 1 0 , 𝑦 = 2
  • D 𝑥 = 1 2 , 𝑦 = 4
  • E 𝑥 = 2 , 𝑦 = 2

Q21:

If 𝑛!=𝐶×𝑃, find 𝑛.

Q22:

If 𝑃=𝐶, find the value(s) of 𝑟.

  • A3 or 4
  • B3
  • C4
  • D2
  • E0 or 1

Q23:

Find the value of 𝐶, given that 𝐶=𝐶 and 𝐶=455.

Q24:

Find 𝑃𝐶.

  • A1
  • B 𝑛 !
  • C ( 𝑛 𝑟 ) !
  • D 𝑟 !
  • E ( 𝑛 1 ) !

Q25:

Using the equations 𝐶𝐶=3413 and 𝑃𝑃=4737 to find the values of 𝑛 and 𝑟, evaluate the expression 𝑛+𝑟.

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