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Quiz Chapter 4: Permutation and Combination

10 questions · Form 5 Additional Mathematics Bab 4: Permutation and Combination

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Calculate the value of ⁶P₃.

  1. 120
  2. 20
  3. 720
  4. 18
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Answer: A

⁶P₃ = 6! / (6 - 3)! = 6! / 3! = 6 × 5 × 4 = 120.

2. Find the value of n if ⁿP₂ = 42.

  1. 7
  2. 6
  3. 8
  4. 9
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Answer: A

ⁿP₂ = n(n - 1) = 42 => n² - n - 42 = 0 => (n - 7)(n + 6) = 0. Since n must be positive, n = 7.

3. If ⁿC₃ = ⁿC₅, find the value of n.

  1. 8
  2. 15
  3. 2
  4. 10
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Answer: A

Using property ⁿC_r = ⁿC_(n-r): n - 3 = 5 => n = 8.

4. A box contains 5 red balls and 4 blue balls. How many ways can 3 balls be selected such that at least 2 red balls are chosen?

  1. 50
  2. 40
  3. 10
  4. 80
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Answer: A

Case 1: 2 red, 1 blue = ⁵C₂ × ⁴C₁ = 10 × 4 = 40. Case 2: 3 red, 0 blue = ⁵C₃ × ⁴C₀ = 10 × 1 = 10. Total ways = 40 + 10 = 50.

5. Find the number of ways to arrange 5 distinct beads on a necklace.

  1. 12
  2. 24
  3. 120
  4. 60
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Answer: A

For a necklace where clockwise and counter-clockwise arrangements are identical: (n - 1)! / 2 = (5 - 1)! / 2 = 242 = 12.

6. A test paper consists of 10 questions divided into Section A (5 questions) and Section B (5 questions). A candidate needs to answer 6 questions, selecting at least 2 from each section. How many different selections can be made?

  1. 200
  2. 210
  3. 100
  4. 252
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Answer: A

Possible distributions (Sec A, Sec B): (2, 4) = ⁵C₂ × ⁵C₄ = 10 × 5 = 50. (3, 3) = ⁵C₃ × ⁵C₃ = 10 × 10 = 100. (4, 2) = ⁵C₄ × ⁵C₂ = 5 × 10 = 50. Total = 50 + 100 + 50 = 200.

7. How many triangles can be formed using the vertices of an octagon?

  1. 56
  2. 336
  3. 24
  4. 112
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Answer: A

An octagon has 8 vertices. Choosing 3 vertices forms a triangle: ⁸C₃ = 8 × 7 × 63 × 2 × 1 = 56.

8. Find the number of ways to arrange 6 people around a circular table.

  1. 120
  2. 720
  3. 360
  4. 24
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Answer: A

Circular permutation = (n - 1)! = (6 - 1)! = 5! = 120.

9. In how many ways can a committee of 4 people be selected from 6 men and 5 women if the committee must consist of 2 men and 2 women?

  1. 150
  2. 330
  3. 450
  4. 75
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Answer: A

Ways to choose 2 men from 6 = ⁶C₂ = 15. Ways to choose 2 women from 5 = ⁵C₂ = 10. Total ways = 15 × 10 = 150.

10. Evaluate ⁴P₄ + ⁴C₄.

  1. 25
  2. 24
  3. 16
  4. 28
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Answer: A

⁴P₄ = 4! = 24. ⁴C₄ = 1. Total = 24 + 1 = 25.

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