10 questions · Form 5 Additional Mathematics Bab 4: Permutation and Combination
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 without repetition?
Answer: A
The last digit must be even (2, 4, or 6): 3 choices. The remaining 3 digits are chosen from the 5 remaining numbers: ⁵P₃ = 60. Total = 3 × 60 = 180.
2. Find the number of signals that can be made using 3 flags of different colors placed one above the other from a set of 7 available flags.
Answer: A
Order matters, so use permutation: ⁷P₃ = 7 × 6 × 5 = 210.
3. In how many ways can the letters of the word 'VECTOR' be arranged such that the vowels are always together?
Answer: A
Vowels in 'VECTOR' are E and O (2 vowels). Group (E, O) as 1 unit. Units to arrange: (EO), V, C, T, R = 5 units. Arrangements of 5 units = 5! = 120. Internal arrangements of E and O = 2! = 2. Total = 120 × 2 = 240.
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?
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 all letters in the word 'SUCCESS'.
Answer: A
Total letters = 7, with S repeating 3 times and C repeating 2 times. Permutations = 7! / (3! × 2!) = 50406 × 2 = 420.
6. 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?
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.
7. Find the number of different ways to arrange all the letters in the word 'MALAYSIA'.
Answer: A
Total letters = 8, with 'A' repeating 3 times. Permutations = 8! / 3! = 403206 = 6720.
8. Find the number of ways to arrange 5 distinct beads on a necklace.
Answer: A
For a necklace where clockwise and counter-clockwise arrangements are identical: (n - 1)! / 2 = (5 - 1)! / 2 = 242 = 12.
9. Given that ⁿC₂ = 28, find the value of n.
Answer: A
ⁿC₂ = nn - 12 = 28 => n(n - 1) = 56 => n² - n - 56 = 0 => (n - 8)(n + 7) = 0. Thus, n = 8.
10. Calculate the value of ⁸C₅.
Answer: A
⁸C₅ = 8! / (5! × 3!) = 8 × 7 × 63 × 2 × 1 = 56.