Help me!

We have a deck of cards (52 cards). Assume we draw 13 cards at random. Calculate the probability having at least a form of four seasons (for example, Heart 3, Diamond 2, Club 2, Spade 2). Thanks a lot.

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- May 18th 2011, 07:58 AMmahefoprobability having at least a four seasons
Help me!

We have a deck of cards (52 cards). Assume we draw 13 cards at random. Calculate the probability having at least a form of four seasons (for example, Heart 3, Diamond 2, Club 2, Spade 2). Thanks a lot. - May 18th 2011, 08:15 AMPlato
Please be more forthcoming as to what "

" means.*a form of four seasons*

What exactly does that mean? - May 18th 2011, 02:25 PMmahefo
It mean a foursome. In a deck of cark, we have 13 foursome. Each foursome consists of four cards of same number. For example, four cards: 9 heart, 9 diamond, 9 club, 9 spade is a foursome.

- May 18th 2011, 02:50 PMPlato
Well that is certainly different from the example in the OP.

There are $\displaystyle \sum\limits_{k = 1}^3 {\left( { - 1} \right)^{k - 1} \binom{13}{k}\binom{52 - 4k}{13 - 4k} $

ways to have**at least one***four of a kind*in a deal of thirteen cards from a standard deck.