🔢 Permutation & Combination

Last Updated: Jan 2026

Permutation and Combination are counting techniques used to find the number of possible arrangements or selections.

  • How many ways?
  • How many arrangements?
  • How many selections?
  • Probability
  • Statistics
  • Algorithms
  • Competitive programming

🗣 Hinglish Tip: Permutation = order matter karta hai, Combination = order matter nahi karta

Permutation

Permutation is the arrangement of objects where order matters.

Permutation Formula

Number of permutations of r objects chosen from n objects:

ⁿPᵣ = n! / (n − r)!

Example 1: Simple Permutation

How many ways can we arrange 3 letters from A, B, C?

n = 3, r = 3

³P₃ = 3! / 0! = 6

Arrangements:

ABC, ACB, BAC, BCA, CAB, CBA

Example 2: Digit Arrangement

How many 2-digit numbers can be formed from digits 1, 2, 3 without repetition?

n = 3, r = 2

³P₂ = 3! / 1! = 6

Permutation with Repetition

If repetition is allowed:

n^r

Example:

  • 2-digit numbers using digits ô1,2,3 ô with repetition:
3^2 = 9

Combination

Combination is the selection of objects where order does NOT matter.

Combination Formula

Number of combinations of r objects chosen from n objects:

ⁿCᵣ = n! / [r!(n − r)!]

Example 3: Simple Combination

From 5 students, how many ways to choose 2 students?

n = 5, r = 2

⁵C₂ = 5! / (2! × 3!) = 10

Key Relationship Between P & C

ⁿPᵣ = ⁿCᵣ × r!

Meaning:

  • Permutation = Combination × arrangements

Key Takeaways

  • Permutation → arrangement
  • Combination → selection
  • Always check: Does order matter?
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