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30 Permutations & Combinations Questions and Answers

30 solved Permutations & Combinations questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced permutations & combinations questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

n! = n × (n-1) × (n-2) × ... × 1 Permutations: nPr = n! / (n-r)! Combinations: nCr = n! / [r!(n-r)!] nC₀ = nCn = 1, nC₁ = n, nCr = nC(n-r) Arrangement with repetitions: n^r
Q1 Medium

How many ways can 3 members be chosen from 12 members?

  • A. 217
  • B. 223
  • C. 220 ✓
  • D. 214
Explanation: Selection uses combination: 12C3 = 220.
Q2 Medium

How many distinct arrangements are possible for letters in 'BOOK'?

  • A. 28
  • B. 20
  • C. 24 ✓
  • D. 16
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q3 Medium

How many ways can 2 members be chosen from 12 members?

  • A. 66 ✓
  • B. 60
  • C. 69
  • D. 63
Explanation: Selection uses combination: 12C2 = 66.
Q4 Medium

How many ways can 4 members be chosen from 9 members?

  • A. 129
  • B. 126 ✓
  • C. 120
  • D. 123
Explanation: Selection uses combination: 9C4 = 126.
Q5 Medium

How many ways can 2 members be chosen from 11 members?

  • A. 58
  • B. 52
  • C. 49
  • D. 55 ✓
Explanation: Selection uses combination: 11C2 = 55.
Q6 Medium

How many ways can 5 members be chosen from 8 members?

  • A. 53
  • B. 50
  • C. 56 ✓
  • D. 59
Explanation: Selection uses combination: 8C5 = 56.
Q7 Medium

How many distinct arrangements are possible for letters in 'QUIZ'?

  • A. 24 ✓
  • B. 28
  • C. 20
  • D. 16
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q8 Medium

How many ways can 5 members be chosen from 10 members?

  • A. 249
  • B. 246
  • C. 252 ✓
  • D. 255
Explanation: Selection uses combination: 10C5 = 252.
Q9 Medium

How many distinct arrangements are possible for letters in 'BOOK'?

  • A. 28
  • B. 24 ✓
  • C. 16
  • D. 20
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q10 Medium

How many ways can 5 members be chosen from 9 members?

  • A. 123
  • B. 126 ✓
  • C. 129
  • D. 120
Explanation: Selection uses combination: 9C5 = 126.
Q11 Medium

How many ways can 2 members be chosen from 10 members?

  • A. 39
  • B. 42
  • C. 45 ✓
  • D. 48
Explanation: Selection uses combination: 10C2 = 45.
Q12 Medium

How many distinct arrangements are possible for letters in 'QUIZ'?

  • A. 24 ✓
  • B. 16
  • C. 20
  • D. 28
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q13 Medium

How many ways can 4 members be chosen from 6 members?

  • A. 12
  • B. 9
  • C. 18
  • D. 15 ✓
Explanation: Selection uses combination: 6C4 = 15.
Q14 Medium

How many distinct arrangements are possible for letters in 'BOOK'?

  • A. 24 ✓
  • B. 28
  • C. 16
  • D. 20
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q15 Medium

How many ways can 4 members be chosen from 8 members?

  • A. 64
  • B. 73
  • C. 67
  • D. 70 ✓
Explanation: Selection uses combination: 8C4 = 70.
Q16 Medium

How many distinct arrangements are possible for letters in 'CODE'?

  • A. 20
  • B. 24 ✓
  • C. 28
  • D. 16
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q17 Medium

How many ways can 2 members be chosen from 8 members?

  • A. 22
  • B. 25
  • C. 31
  • D. 28 ✓
Explanation: Selection uses combination: 8C2 = 28.
Q18 Medium

How many ways can 3 members be chosen from 8 members?

  • A. 59
  • B. 56 ✓
  • C. 50
  • D. 53
Explanation: Selection uses combination: 8C3 = 56.
Q19 Medium

How many distinct arrangements are possible for letters in 'CODE'?

  • A. 28
  • B. 16
  • C. 20
  • D. 24 ✓
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q20 Medium

How many ways can 5 members be chosen from 6 members?

  • A. 0
  • B. 9
  • C. 3
  • D. 6 ✓
Explanation: Selection uses combination: 6C5 = 6.
Q21 Medium

How many ways can 4 members be chosen from 9 members?

  • A. 123
  • B. 126 ✓
  • C. 129
  • D. 120
Explanation: Selection uses combination: 9C4 = 126.
Q22 Medium

How many distinct arrangements are possible for letters in 'MATH'?

  • A. 28
  • B. 16
  • C. 20
  • D. 24 ✓
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q23 Medium

How many ways can 5 members be chosen from 11 members?

  • A. 465
  • B. 456
  • C. 462 ✓
  • D. 459
Explanation: Selection uses combination: 11C5 = 462.
Q24 Medium

How many distinct arrangements are possible for letters in 'BOOK'?

  • A. 28
  • B. 20
  • C. 16
  • D. 24 ✓
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q25 Medium

How many ways can 3 members be chosen from 6 members?

  • A. 14
  • B. 17
  • C. 20 ✓
  • D. 23
Explanation: Selection uses combination: 6C3 = 20.
Q26 Medium

How many distinct arrangements are possible for letters in 'MATH'?

  • A. 24 ✓
  • B. 28
  • C. 16
  • D. 20
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q27 Medium

How many ways can 5 members be chosen from 12 members?

  • A. 786
  • B. 795
  • C. 789
  • D. 792 ✓
Explanation: Selection uses combination: 12C5 = 792.
Q28 Medium

How many ways can 4 members be chosen from 9 members?

  • A. 126 ✓
  • B. 123
  • C. 120
  • D. 129
Explanation: Selection uses combination: 9C4 = 126.
Q29 Medium

How many ways can 4 members be chosen from 12 members?

  • A. 492
  • B. 489
  • C. 495 ✓
  • D. 498
Explanation: Selection uses combination: 12C4 = 495.
Q30 Medium

How many distinct arrangements are possible for letters in 'CODE'?

  • A. 20
  • B. 16
  • C. 28
  • D. 24 ✓
Explanation: All letters are distinct. Arrangements = 4! = 24.

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