NUST NET Maths chapter 5: Maths · Permutations, combinations and probability MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

16 exam-style questions on Maths · Permutations, combinations 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.

16 questions · 2 topics · 10 per test

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What chapter 5 covers

Ten Maths · Permutations, combinations 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. In how many ways can 8 people sit at a round table if two particular people must sit together?

  1. A
    1440
  2. B
    720
  3. C
    10080
  4. D
    5040
Show answer

Answer: A. Treat the pair as one unit: 7 units round a table in (7 − 1)! = 720 ways, and the pair can swap seats in 2 ways, giving 1440. Forgetting the swap gives 720.

2. In how many ways can 5 boys and 3 girls sit in a row so that no two girls sit next to each other?

  1. A
    4320
  2. B
    14400
  3. C
    2400
  4. D
    40320
Show answer

Answer: B. Seat the boys in 5! = 120 ways; this makes 6 gaps (ends included). The girls fill 3 of these gaps in 6P3 = 120 ways, so the total is 120 × 120 = 14400.

3. A committee of 4 is to be chosen from 6 men and 4 women so that it has at least 3 women. The number of ways is

  1. A
    24
  2. B
    28
  3. C
    25
  4. D
    210
Show answer

Answer: C. Exactly 3 women: 4C3 × 6C1 = 24; all 4 women: 1 way. Total 24 + 1 = 25. Choosing 3 women and then any 1 of the other 7 (giving 28) counts some committees twice.

4. Three fair coins are tossed. The probability of getting at least two heads is

  1. A
    3/8
  2. B
    7/8
  3. C
    1/4
  4. D
    1/2
Show answer

Answer: D. Of the 8 outcomes, HHT, HTH, THH and HHH have at least two heads, so P = 4/8 = 1/2. 3/8 counts exactly two heads only.

5. The number of different arrangements of all the letters of the word ENGINEERING is

  1. A
    11!/(3! 3!)
  2. B
    11!/(3! 3! 2!)
  3. C
    11!
  4. D
    11!/(3! 3! 2! 2!)
Show answer

Answer: D. ENGINEERING has 11 letters: E three times, N three times, G twice, I twice and R once. Divide 11! by the factorial of each repeat count.

6. How many 3-digit numbers with no repeated digit can be formed from the digits 0, 1, 2, 3, 4?

  1. A
    60
  2. B
    100
  3. C
    48
  4. D
    36
Show answer

Answer: C. The hundreds digit cannot be 0, so it has 4 choices; the tens and units digits then have 4 and 3 choices: 4 × 4 × 3 = 48. 5P3 = 60 wrongly includes arrangements starting with 0.

7. For events A and B, P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. The probability that neither A nor B occurs is

  1. A
    0.1
  2. B
    0.7
  3. C
    0.8
  4. D
    0.3
Show answer

Answer: D. P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7, so P(neither) = 1 − 0.7 = 0.3. Forgetting to subtract P(A ∩ B) gives 1 − 0.9 = 0.1.

8. Two fair dice are thrown. The probability that the two numbers are different is

  1. A
    1/6
  2. B
    5/6
  3. C
    5/12
  4. D
    5/7
Show answer

Answer: B. The doublets (1, 1), ..., (6, 6) are 6 of the 36 outcomes, so P = 1 − 6/36 = 5/6. Counting unordered pairs (15 out of 21) gives 5/7, but those 21 pairs are not equally likely.

9. An integer is chosen at random from 1 to 100. The probability that it is divisible by 3 or 5 is

  1. A
    47/100
  2. B
    53/100
  3. C
    7/15
  4. D
    33/100
Show answer

Answer: A. There are 33 multiples of 3, 20 multiples of 5 and 6 multiples of 15, so 33 + 20 − 6 = 47 numbers qualify. Forgetting to subtract the multiples of 15 gives 53/100.

10. Each of 12 people shakes hands once with every other person. The total number of handshakes is

  1. A
    132
  2. B
    66
  3. C
    144
  4. D
    78
Show answer

Answer: B. A handshake is a selection of 2 people: 12C2 = (12 × 11)/2 = 66. 12 × 11 = 132 counts every handshake twice.

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Ways to practise this chapter

Maths · Permutations, combinations and probability: questions students ask

How many Maths · Permutations, combinations and probability MCQs are there?

16, each with the answer and a short explanation, across 2 topics: Permutations and combinations, Probability. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 5 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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