# probability having at least a four seasons

• May 18th 2011, 08:58 AM
mahefo
probability 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, 09:15 AM
Plato
Please be more forthcoming as to what "a form of four seasons " means.
What exactly does that mean?
• May 18th 2011, 03:25 PM
mahefo
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, 03:50 PM
Plato
Quote:

Originally Posted by mahefo
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.

Well that is certainly different from the example in the OP.
There are $\sum\limits_{k = 1}^3 {\left( { - 1} \right)^{k - 1} \binom{13}{k}\binom{52 - 4k}{13 - 4k}$
ways to have at least one four of a kind in a deal of thirteen cards from a standard deck.