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Probability

Inviting four of ten friends to dinner

countingcombinations

You want to invite 44 friends to dinner and have 1010 friends to choose from. A guest list is just a set of people, so order does not matter.

How many different guest lists of 44 are possible?

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The theory behind this question.

Balls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingCatalan NumbersCounting: Permutations and Combinations

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