Permutation vs Combination Basic Theory

Let's break it down in a simple way with examples.

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Permutation vs Combination

Both permutation and combination are ways to select items from a group, but:

• Permutation → Order matters
• Combination → Order does NOT matter

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1. Permutation (Order Matters)

If you have N items and you want to pick R items where order matters

Example:

You have A, B, C, and you want to select 2 letters in different orders.

Possible selections:
AB, BA, AC, CA, BC, CB (Different order matters!)

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2. Combination (Order Doesn’t Matter)

If you have N items and you want to pick R items where order does NOT matter

Example:

You have A, B, C, and you want to select 2 letters, but order doesn’t matter.

Possible selections:
AB, AC, BC (Here, AB is the same as BA)

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How This Applies to LeetCode Coding Problems

1. Use Permutations when order matters

   • Example: Generating all possible orderings of a list ([1,2,3] → [1,2,3], [1,3,2], [2,1,3] etc.)
   • LeetCode problem: "Permutations" (Backtracking)

2. Use Combinations when order does NOT matter

   • Example: Picking subsets ([1,2,3] → {1,2}, {1,3}, {2,3})
   • LeetCode problem: "Combinations" (Backtracking)

When to Use Which?

• Use permutations when solving problems like arranging numbers or letters in different orders.
• Use combinations when selecting elements without worrying about order.

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Quick Mnemonic
👉 Permutation = Position matters
👉 Combination = Choice matters, but order doesn't