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Concept Breakdowns

Counting Permutations vs Combinations

Permutations and combinations are the two fundamental counting techniques in discrete math and probability. These flashcards clarify when order matters (permutations) vs. when it doesn't (combinations), covering formulas, typical exam problems, and common student errors on CS and math exams.

Interactive Deck

5 Cards
1
Front

What is a permutation?

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1
Back

Permutation: An ordered arrangement of r items from n. Formula: P(n,r) = n! / (n-r)!. Use when order matters, e.g., ranking contestants.

2
Front

What is a combination?

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2
Back

Combination: An unordered selection of r items from n. Formula: C(n,r) = n! / (r! * (n-r)!). Use when order does not matter, e.g., choosing a team.

3
Front

When to use permutation vs combination?

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3
Back

Ask: does swapping items give a different outcome? If yes, use permutation. If no, use combination.

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Locked

Permutation with repetition formula

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Combination with repetition formula

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Frequently Asked Questions

What is the difference between permutation and combination?

Permutation counts ordered arrangements — sequence matters. Combination counts unordered selections — only membership matters.

  • Permutation: P(n,r) = n!/(n-r)!
  • Combination: C(n,r) = n!/(r!(n-r)!)
  • P(n,r) = r! * C(n,r)

How do I know which formula to use?

Ask: if I rearrange the selected items, is the outcome different? If yes — permutation. If no — combination. Example: a password is a permutation; a committee is a combination.

What is 0! and why does it equal 1?

By convention, 0! = 1. This ensures the permutation and combination formulas work correctly when all n items are selected (r = n), since P(n,n) = n! and C(n,n) = 1.

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