Shortcut Techniques

Permutations & Combinations

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Permutations & Combinations

⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.

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Shortcut Techniques

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Shortcut Techniques – Permutations & Combinations

Shortcut techniques in Permutations & Combinations help candidates solve arrangement and selection problems quickly and accurately in SSC, Banking, Railway, CAT, NDA, CDS, Insurance, Defence, and various competitive examinations.

This chapter is extremely important because it forms the foundation for:

  • Probability
  • Seating Arrangement
  • Word Formation
  • Selection Problems
  • Distribution Problems
  • Advanced Counting Techniques

Learning shortcut methods reduces lengthy calculations and improves solving speed significantly.

Golden Rule of This Chapter

Permutation → Arrangement

Combination → Selection

Shortcut #1: Identify Whether Order Matters

If Question Says Use
Arrange, Seat, Rank Permutation
Select, Choose, Form Committee Combination

✔ This is the most important shortcut in the chapter.

Shortcut #2: Memorize Basic Permutation Formula

nPr = n! / (n-r)!

Use when:

  • Order matters
  • Arrangement is required

Shortcut #3: Memorize Basic Combination Formula

nCr = n! / [r!(n-r)!]

Use when:

  • Selection is required
  • Order does not matter

Shortcut #4: Direct Relation Shortcut

nPr = nCr × r!

Very useful in advanced aptitude questions.

Shortcut #5: Learn Important Factorials

Factorial Value
0! 1
1! 1
2! 2
3! 6
4! 24
5! 120
6! 720
7! 5040
8! 40320

✔ Memorizing factorials saves significant calculation time.

Shortcut #6: Circular Arrangement Trick

For arranging n objects in a circle:

(n − 1)!

Reason:

In circular arrangements, one position is fixed.

Shortcut #7: Repetition Allowed Shortcut

If repetition is allowed:

nr

where:

  • n = Available objects
  • r = Positions

Shortcut #8: Repeated Objects Formula

If some letters or objects repeat:

N! / (P! × Q! × R!)

Example:

BANANA

  • A repeats 3 times
  • N repeats 2 times

Shortcut #9: Combination Symmetry Trick

nCr = nCn-r

Choose the smaller value for easier calculations.

Example:

10C8 = 10C2

Shortcut #10: Special Combination Values

Formula Value
nC0 1
nC1 n
nCn 1

Shortcut #11: Arrangement of Digits Trick

For arranging digits without repetition:

  • First place has maximum choices
  • Choices decrease gradually

Example:

4-digit numbers using 1,2,3,4:

= 4 × 3 × 2 × 1

= 24

Shortcut #12: Numbers Beginning with Zero

Zero cannot come at the beginning of a number.

Always fix non-zero digit first.

Shortcut #13: Committee Formation Trick

Committee problems always use combinations because:

  • Only selection matters
  • Order is irrelevant

Shortcut #14: Seating Arrangement Trick

Seating arrangement questions always use permutations because:

  • Position changes matter
  • Order matters

Shortcut #15: Word Formation Trick

If letters repeat:

  • Use repeated object formula
  • Avoid counting duplicate arrangements

Shortcut #16: Quick Cancellation Trick

Cancel factorials quickly:

Example:

8! / 6!

= 8 × 7

= 56

Shortcut #17: Large Combination Simplification

Use symmetry property:

20C18 = 20C2

This reduces lengthy calculations.

Shortcut #18: Distinguish Arrangement vs Selection Quickly

Question Type Use
How many ways to arrange? Permutation
How many ways to select? Combination
How many teams? Combination
How many seatings? Permutation

Shortcut #19: Quick Revision Formula Table

Concept Shortcut Formula
Permutation nPr = n!/(n-r)!
Combination nCr = n!/[r!(n-r)!]
Circular Permutation (n−1)!
Repetition Allowed nr
Repeated Objects N!/(P!Q!R!)
Relation nPr = nCr × r!

Shortcut #20: Most Important Exam Tricks

  • Order matters → Permutation
  • Order does not matter → Combination
  • Use symmetry property for easy calculations.
  • Memorize factorial values.
  • Use cancellation methods wherever possible.
  • Read arrangement conditions carefully.
  • Practice repeated object problems regularly.

Common Mistakes to Avoid

  • Using permutation instead of combination.
  • Ignoring repeated objects.
  • Using wrong factorial calculations.
  • Ignoring circular arrangement rules.
  • Allowing zero at starting position.

Important Exam Tips

  • Read the question carefully before choosing formula.
  • Practice arrangement and selection separately.
  • Memorize important formulas thoroughly.
  • Improve factorial simplification speed.
  • Use symmetry property whenever possible.
  • Practice previous year aptitude questions regularly.
  • Verify calculations carefully.

Shortcut techniques in Permutations & Combinations help candidates improve solving speed, reduce lengthy calculations, and solve arrangement and selection aptitude questions efficiently in competitive examinations.

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