Worksheet: Properties of Combinations

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

Q1:

Evaluate 𝐶 𝐶 .

  • A 5 6 0 1
  • B 3 2 8
  • C 1 5 6 0
  • D 2 8 3
  • E 2 2 4 1

Q2:

Evaluate 𝐶 .

Q3:

Evaluate 𝐶 + 𝐶 .

Q4:

Find the value of 𝑥 such that 𝐶 = 3 , 0 6 0 and 𝐶 = 𝐶 .

Q5:

Find 𝑟 given that 𝐶 > 1 and 𝐶 > 1 .

Q6:

Find the value of 𝐶 𝐶 + 𝐶 𝐶 + 𝐶 .

Q7:

If 𝐶 = 1 2 0 , find 𝑛 .

Q8:

If 𝐶 = 3 5 , find 𝐶 .

Q9:

If ( 3 𝑛 5 ) ! = 2 4 , find 𝐶 .

Q10:

Given that 𝑛 3 𝐶 = 2 𝑛 , evaluate 𝑛 3 𝐶 .

Q11:

Given that , determine .

Q12:

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

Q13:

If 𝐶 = 2 and 𝐶 = 2 1 , find ( 𝑛 𝑚 ) ! .

Q14:

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

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

Q15:

If 𝑛 ! = 5 , 0 4 0 and 𝐶 = 7 0 , find 𝐶 + 𝐶 .

Q16:

Find the value of 𝐶 + 𝐶 + 𝐶 + + 𝐶 .

Q17:

Evaluate 𝐶 .

Q18:

Find the value of 𝐶 + 𝐶 𝐶 .

Q19:

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

  • A3
  • B3 or 9
  • C9
  • D3 or 6
  • E6

Q20:

Evaluate 𝐶 .

Q21:

If 𝑃 = 5 , 4 0 2 , and 𝐶 = 1 0 4 , find 𝑚 and 𝑛 .

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

Q22:

Given that , determine and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q23:

Given that 𝑃 𝐶 = 2 0 ! and 𝐶 𝐶 = 5 1 9 , find 𝑛 and 𝑟 .

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

Q24:

Which of the following is equal to 𝐶 ?

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

Q25:

Determine the value of 𝐶 𝐶 without using a calculator.

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

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