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15 Permutations & Combinations Questions and Answers

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

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Practice permutations & combinations questions with detailed explanations. These solved examples cover the most frequently asked patterns in placement and competitive exams.

Q1 Easy

Find 10P4.

  • A. 5045
  • B. 5040 ✓
  • C. 5030
  • D. 5035
Explanation: nPr = n!/(n-r)! = 5040.
Q2 Easy

Find 10P3.

  • A. 720 ✓
  • B. 725
  • C. 710
  • D. 715
Explanation: nPr = n!/(n-r)! = 720.
Q3 Easy

Find 8P4.

  • A. 1675
  • B. 1680 ✓
  • C. 1685
  • D. 1670
Explanation: nPr = n!/(n-r)! = 1680.
Q4 Easy

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

  • A. 24 ✓
  • B. 16
  • C. 20
  • D. 28
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q5 Easy

Find 7P2.

  • A. 42 ✓
  • B. 37
  • C. 47
  • D. 32
Explanation: nPr = n!/(n-r)! = 42.
Q6 Easy

Find 8P3.

  • A. 326
  • B. 336 ✓
  • C. 341
  • D. 331
Explanation: nPr = n!/(n-r)! = 336.
Q7 Medium

Find 10P2.

  • A. 80
  • B. 90 ✓
  • C. 85
  • D. 95
Explanation: nPr = n!/(n-r)! = 90.
Q8 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.
Q9 Medium

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

  • A. 255
  • B. 252 ✓
  • C. 246
  • D. 249
Explanation: Selection uses combination: 10C5 = 252.
Q10 Medium

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

  • A. 28
  • B. 16
  • C. 20
  • D. 24 ✓
Explanation: All letters are distinct. Arrangements = 4! = 24.
Q11 Medium

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

  • A. 214
  • B. 223
  • C. 217
  • D. 220 ✓
Explanation: Selection uses combination: 12C3 = 220.
Q12 Hard

Find 9P2.

  • A. 62
  • B. 77
  • C. 72 ✓
  • D. 67
Explanation: nPr = n!/(n-r)! = 72.
Q13 Hard

How many ways can 2 members be chosen from 9 members?

  • A. 33
  • B. 30
  • C. 36 ✓
  • D. 39
Explanation: Selection uses combination: 9C2 = 36.
Q14 Hard

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.
Q15 Hard

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

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

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