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Tuesday, July 9, 2013

Draw 5 card, how many combination that result contains at least 1 king.?

From a common deck of 52 cards containing 4 kings, how many combination of drawing 5 cards and the result contains at least 1 king.

Or generally, from any deck of k cards containing n specific kind of cards, how many combination of drawing r cards and the result contains at least 1 card of that kind.

I have attempted to find the formula, but I am not sure that it is correct.

My solution is: summation from [i=1] to [min(n, r)] of [nCi]

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