🔢 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:

${}^nP_r = \frac{n!}{(n-r)!}$

Example 1: Simple Permutation

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

n = 3, r = 3

${}^3P_3 = \frac{3!}{0!} = 6$

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

${}^3P_2 = \frac{3!}{1!} = 6$

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:

${}^nC_r = \frac{n!}{r!(n-r)!}$

Example 3: Simple Combination

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

n = 5, r = 2

${}^5C_2 = \frac{5!}{2! \times 3!} = 10$

Key Relationship Between P & C

${}^nP_r = {}^nC_r \times r!$

Meaning:

• Permutation = Combination x arrangements

Key Takeaways

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

Liked This Tutorial

Scan QR Code To Leave A Review Or

Click Here To Leave A Review