PMA Long Course Mathematics: Permutation & Combination MCQs

PMA Long Course Mathematics: Permutation & Combination MCQs — sample questions

1. Question 1

   Q1. In how many ways can 5 boys and 3 girls be seated in a row such that no two girls are together?

   • A) 6! * 7C3
   • B) 5! * 6C3 * 3!
   • C) 6! * 7P3
   • D) 5! * 6P3

   Answer: 5! * 6C3 * 3!

   Explanation: First arrange 5 boys in 5! ways, then select 3 places out of 6 for girls in 6C3 ways, and arrange them in 3! ways.

2. Question 2

   Q2. A bag contains 4 red and 6 black balls. One ball is drawn at random. What is the probability that it is red?

   • A) 4 / 10
   • B) 6 / 10
   • C) 2 / 5
   • D) Both A and C

   Answer: Both A and C

   Explanation: Total balls = 10, red balls = 4, probability = 4/10 = 2/5.

3. Question 3

   Q3. The number of ways to choose 3 or more books from a shelf of 7 books is

   • A) 7C3 + 7C4 + 7C5 + 7C6 + 7C7
   • B) 2^7 - (7C0 + 7C1 + 7C2)
   • C) Both A and B
   • D) 7P3 + 7P4 + 7P5 + 7P6 + 7P7

   Answer: Both A and B

   Explanation: Both methods count the number of subsets with 3 or more elements: directly and by subtracting subsets with 0, 1, or 2 elements from total subsets.

4. Question 4

   Q4. A committee of 5 is to be formed from 6 men and 4 women. In how many ways can this be done if at least 2 women are included?

   • A) 6C3 * 4C2 + 6C2 * 4C3 + 6C1 * 4C4
   • B) 4C2 * 6C3 + 4C3 * 6C2 + 4C4 * 6C1
   • C) Both A and B
   • D) 10C5 - (4C0 * 6C5 + 4C1 * 6C4)

   Answer: Both A and B

   Explanation: Count committees with 2, 3, or 4 women and corresponding men, or use the complementary counting principle.

5. Question 5

   Q5. The probability that a leap year has 53 Sundays is

   • A) 1 / 7
   • B) 2 / 7
   • C) 3 / 7
   • D) 4 / 7

   Answer: 2 / 7

   Explanation: A leap year has 52 weeks and 2 extra days. For 53 Sundays, one of the extra days must be Sunday, probability = 2/7.