FSc Part 1 Maths chapter 7: Permutation, combination and probability MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

29 exam-style questions on Permutation, combination and probability, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

29 questions · 3 topics · 10 per test

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What chapter 7 covers

Ten Permutation, combination and probability questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Two fair coins are tossed. The probability of getting at least one head is

  1. A
    2/3
  2. B
    1/2
  3. C
    1/4
  4. D
    3/4
Show answer

Answer: D. The sample space is {HH, HT, TH, TT}. Three outcomes contain a head, so P = 3/4. 2/3 comes from wrongly listing only 3 outcomes.

2. The relation between nPr and nCr is

  1. A
    nPr = nCr ÷ r!
  2. B
    nCr = r! × nPr
  3. C
    nPr = n! × nCr
  4. D
    nPr = r! × nCr
Show answer

Answer: D. Each selection of r objects can be arranged in r! orders, so there are r! times as many permutations as combinations.

3. The number of diagonals of a hexagon is

  1. A
    12
  2. B
    15
  3. C
    6
  4. D
    9
Show answer

Answer: D. Lines joining 2 of the 6 vertices: 6C2 = 15. Six of these are sides, leaving 15 − 6 = 9 diagonals.

4. The value of 7P3 is

  1. A
    210
  2. B
    35
  3. C
    343
  4. D
    5040
Show answer

Answer: A. 7P3 = 7!/4! = 7 × 6 × 5 = 210. 35 is 7C3, which ignores order.

5. In how many ways can a committee of 3 be chosen from 8 people?

  1. A
    336
  2. B
    56
  3. C
    24
  4. D
    512
Show answer

Answer: B. Order does not matter in a committee: 8C3 = (8 × 7 × 6)/6 = 56. 336 is 8P3.

6. The value of 0! is

  1. A
    undefined
  2. B
    0
  3. C
    1
  4. D
    −1
Show answer

Answer: C. 0! is defined as 1, which keeps formulas such as nPn = n!/0! = n! correct.

7. There are 3 roads from town A to town B and 4 roads from B to C. The number of ways to travel from A to C through B is

  1. A
    81
  2. B
    7
  3. C
    64
  4. D
    12
Show answer

Answer: D. By the fundamental principle of counting, the choices multiply: 3 × 4 = 12. Adding (7) would be for choosing one road from either set.

8. In how many ways can 6 people be seated at a round table?

  1. A
    120
  2. B
    720
  3. C
    60
  4. D
    360
Show answer

Answer: A. Circular arrangements of n objects: (n − 1)! = 5! = 120. Fixing one person removes the rotations that look the same.

9. Two fair dice are thrown. The probability of a six on the first die and an odd number on the second is

  1. A
    1/36
  2. B
    2/3
  3. C
    1/3
  4. D
    1/12
Show answer

Answer: D. The dice are independent: P = 1/6 × 3/6 = 1/12. Adding the probabilities gives 2/3, which is not the "and" rule.

10. A and B are independent events with P(A) = 0.4 and P(B) = 0.5. Then P(A ∩ B) is

  1. A
    0.45
  2. B
    0.9
  3. C
    0.1
  4. D
    0.2
Show answer

Answer: D. For independent events P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.

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Ways to practise this chapter

Permutation, combination and probability: questions students ask

How many Permutation, combination and probability MCQs are there?

29, each with the answer and a short explanation, across 3 topics: Factorials and permutations, Combinations, Probability. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 7 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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