Permutations and combinations are methods of counting arrangements and selections. Permutations count ordered arrangements where order matters. Combin
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What is the difference between arranging 3 people in 3 seats vs. selecting 3 people from 5?
Arranging 3 specific people in 3 seats uses permutation formula. Selecting 3 from 5 uses combination formula because selection does not depend on order. If we then arrange the 3 selected people, we multiply combination by permutation.
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Why does n! include 0! = 1?
0! = 1 by definition, which makes many formulas work correctly. It represents one way to arrange zero objects (doing nothing). This definition ensures formulas like nPn = n! and nCn = 1 remain consistent.
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When solving a problem, how do I know if I should use permutation or combination?
Ask yourself: Does the order in which I select or arrange matter? If YES, use permutation (nPr). If NO, use combination (nCr). Example: Seating order matters (permutation); committee selection doesn't (combination).
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