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Easy: nPr and nCr
A permutation counts ordered arrangements: nPr = n! ÷ (n − r)!, such as giving out first, second and third prizes. A combination counts selections where order doesn't matter: nCr = n! ÷ (r!(n − r)!), such as choosing a committee. Ask whether swapping two chosen items gives something different; if it does, order matters.
Find the number of ways.
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Ask whether order matters. Choosing a president and vice-president is a permutation; choosing a two-person committee is a combination.
Each group of r items can be ordered r! ways, and a combination counts all of them once. So C(n, r) = P(n, r)/r!.
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