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Worksheet: Combination Formula

Q1:

Determine the value of 2 3 8 2 3 6 𝐢 𝐢 without using a calculator.

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

Q2:

Determine the value of 2 1 7 2 1 6 𝐢 𝐢 without using a calculator.

  • A 7 6
  • B 7 1 5
  • C 7 3
  • D 1 5 7
  • E 1 3 6

Q3:

Given that 𝑛 + 1 9 π‘₯ + 1 9 𝑛 + 1 9 π‘₯ + 1 8 𝐢 ∢ 𝐢 = 2 ∢ 1 , determine 𝑛 .

  • A π‘₯ + 3 9
  • B π‘₯ + 3 7
  • C 3 π‘₯ + 3 9
  • D 3 π‘₯ + 3 7

Q4:

Find the possible values of π‘Ÿ which satisfy the equation 2 1 π‘Ÿ 2 1 1 5 𝐢 = 𝐢 .

  • A15
  • B15 or 21
  • C21
  • D15 or 6
  • E6

Q5:

Using the equations 𝑛 π‘Ÿ + 3 𝑛 π‘Ÿ + 2 𝐢 ∢ 𝐢 = 3 4 ∢ 1 3 and 𝑛 + 1 π‘Ÿ 𝑛 π‘Ÿ 𝑃 ∢ 𝑃 = 4 7 ∢ 3 7 to find the values of 𝑛 and π‘Ÿ , evaluate the expression 𝑛 + π‘Ÿ .

Q6:

Find the value of 𝑛 given that 𝑛 1 8 𝑛 1 7 𝐢 ∢ 𝐢 = 2 ∢ 1 .

Q7:

Write       𝐢 + 𝐢 in the form   𝐢 .

  • A     𝐢
  • B     𝐢
  • C       𝐢
  • D       𝐢

Q8:

By applying the relation 𝑛 π‘Ÿ 𝑛 π‘Ÿ βˆ’ 1 𝑛 + 1 π‘Ÿ 𝐢 + 𝐢 = 𝐢 , deduce the value of 5 9 2 5 9 3 𝐢 + 𝐢 .

Q9:

Given that 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 𝑛 𝐢 + 𝐢 + 𝐢 + 𝐢 + 𝐢 + 𝐢 + 𝐢 + 𝐢 = 2 , determine the value of 𝑛 .

Q10:

Evaluate          𝐢 + 2 Γ— 𝐢 + 𝐢 .

Q11:

Evaluate 1 6 2 1 6 3 1 7 2 𝐢 + 𝐢 𝐢 .

  • A 1 4 3
  • B 1 5
  • C 3 1 4
  • D5
  • E7

Q12:

If 2 7 π‘Ÿ + 8 2 7 π‘Ÿ + 9 𝐢 ∢ 𝐢 = 6 ∢ 1 and 𝑛 + 1 0 π‘Ÿ βˆ’ 1 1 𝑛 + 1 0 π‘Ÿ βˆ’ 1 0 𝐢 + 𝐢 = 3 3 6 4 9 , find 𝑛 and π‘Ÿ .

  • A 𝑛 = 2 2 , π‘Ÿ = βˆ’ 3
  • B 𝑛 = 1 2 , π‘Ÿ = 1 1
  • C 𝑛 = 2 2 , π‘Ÿ = 1 1
  • D 𝑛 = 1 2 , π‘Ÿ = 1 5

Q13:

Find all of the possible values of 𝑛 , given that 4 Γ— 𝐢 = 3 Γ— 𝐢 + 2 Γ— 𝐢 𝑛 5 𝑛 6 𝑛 4 .

  • A8
  • B13, 11
  • C9
  • D9, 8

Q14:

Given that 𝑛 π‘Ÿ 𝑛 π‘Ÿ + 1 𝑛 π‘Ÿ 𝐢 + 𝐢 𝐢 = 𝑛 + 1 π‘Ÿ + 1 and 𝑛 2 1 𝑛 2 2 𝑛 2 1 𝐢 + 𝐢 𝐢 = 3 2 , find 𝑛 .

Q15:

If 𝑛 4 2 𝑛 𝑛 βˆ’ 4 2 𝑛 4 3 𝐢 + 𝐢 = 2 𝐢 , find 𝑛 .

Q16:

If 1 3 2 π‘Ÿ βˆ’ 9 1 3 π‘Ÿ + 1 𝐢 = 𝐢 , determine π‘Ÿ .

  • A10, 21
  • B8, 2
  • C9, 1
  • D10, 7

Q17:

Find the value of π‘Ÿ such that 1 5 2 π‘Ÿ βˆ’ 4 1 5 π‘Ÿ + 3 𝐢 = 𝐢 .

Q18:

Given that 2 9 3 π‘Ÿ βˆ’ 6 2 9 2 π‘Ÿ 𝐢 = 𝐢 , determine all the possible values of π‘Ÿ .

  • A6
  • B6 or 29
  • C7
  • D6 or 7
  • E29

Q19:

Find the value of 𝑛 5 π‘Ÿ + 2 𝐢 , given that 𝑛 π‘Ÿ + 4 π‘Ÿ 𝑛 4 π‘Ÿ βˆ’ 5 𝐢 = 𝐢 2 and 𝑛 1 2 𝐢 = 4 5 5 .

Q20:

Given that , determine and .

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

Q21:

Find π‘₯ and 𝑦 , such that π‘₯ 𝑦 π‘₯ 𝑦 + 1 𝐢 = 3 8 Γ— 𝐢 and π‘₯ 𝑦 π‘₯ 𝑦 + 6 𝐢 = 𝐢 .

  • A π‘₯ = 2 , 𝑦 = 2
  • B π‘₯ = 4 , 𝑦 = 2
  • C π‘₯ = 1 2 , 𝑦 = 4
  • D π‘₯ = 1 0 , 𝑦 = 2
  • E π‘₯ = 9 , 𝑦 = 2

Q22:

Using the equation 𝑛 π‘Ÿ 𝑛 π‘Ÿ βˆ’ 1 𝑛 π‘Ÿ βˆ’ 2 𝑛 + 2 π‘Ÿ 𝐢 + 2 Γ— 𝐢 + 𝐢 = 𝐢 , evaluate the expression 2 4 2 1 2 4 2 0 2 4 1 9 𝐢 + 2 Γ— 𝐢 + 𝐢 .

  • A 2 4 2 0 𝐢
  • B 2 4 2 1 𝐢
  • C 2 4 1 9 𝐢
  • D 2 6 2 1 𝐢

Q23:

Which of the following is equal to 𝑛 1 6 𝑛 6 7 𝑛 7 𝐢 Γ— 𝐢 𝐢 ?

  • A 6 𝑛 6 7 𝑛 βˆ’ 7 6 𝑃 𝑃
  • B 6 𝑛 6 7 𝑛 βˆ’ 1 7 𝑃 𝑃
  • C 6 𝑛 6 7 𝑛 βˆ’ 7 7 𝑃 𝑃
  • D 6 𝑛 6 7 𝑛 βˆ’ 1 6 𝑃 𝑃

Q24:

If 𝑛 4 𝐢 = 1 5 , determine 2 𝑛 𝑛 + 4 𝐢 .

Q25:

Evaluate 7 2 8 6 𝐢 𝐢 .

  • A 1 4 8 0
  • B 4 3
  • C480
  • D 3 4
  • E 1 1 6 0