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Lesson Worksheet: Properties of Combinations Mathematics

In this worksheet, we will practice using the properties of combinations to simplify expressions and solve equations.

Q1:

Determine the value of 𝐶𝐶 without using a calculator.

  • A734
  • B43
  • C73
  • D52
  • E347

Q2:

If 𝑃=𝐶, find the value(s) of 𝑟.

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

Q3:

Which of the following is equal to 𝐶×𝐶𝐶?

  • A𝑃𝑃
  • B𝑃𝑃
  • C𝑃𝑃
  • D𝑃𝑃

Q4:

Write 𝐶+𝐶 in the form 𝐶.

  • A𝐶
  • B𝐶
  • C𝐶
  • D𝐶

Q5:

Find the possible values of 𝑟 which satisfy the equation 𝐶=𝐶.

  • A15 or 6
  • B15 or 21
  • C15
  • D6
  • E21

Q6:

If 𝐶+𝐶=2𝐶, find 𝑛.

Q7:

Given that 3×𝐶,4×𝐶,6×𝐶, is an arithmetic sequence, find all possible values of 𝑛.

  • A𝑛=21, 𝑛=16
  • B𝑛=22, 𝑛=16
  • C𝑛=22, 𝑛=15
  • D𝑛=21, 𝑛=15

Q8:

Determine the value of 𝐶+𝐶.

  • A𝐶
  • B𝐶
  • C𝐶
  • D𝐶

Q9:

Find the value of 𝐶+𝐶+𝐶++𝐶.

Q10:

Find the value of 𝐶𝐶+𝐶𝐶+𝐶.

This lesson includes 78 additional questions and 450 additional question variations for subscribers.

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