Discrete math

mina4eva

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For a hand of 6 cards, with 52 cards in a deck (13 cards in each suit , with 4 suits)

How many different hands have three or more cards from the same suit?

How many different hands have two cards from three different suits?
 

Subhotosh Khan

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For a hand of 6 cards, with 52 cards in a deck (13 cards in each suit , with 4 suits)

How many different hands have three or more cards from the same suit?

How many different hands have two cards from three different suits?
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Jomo

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How many different hands have three cards from the same suit?
If I gave you a deck of cards how would you make the six card hand I listed above. That is precisely what decisions would you make? Perhaps it would be better to ask if you were going to tell someone to pick these 6 cards what would you tell them to do? Your answer must be perfect, that is the person picking the cards can only do what you tell them.

I will give you an example of what I mean. Suppose in a 5-card hand you want a full-house, that is 3 of one kind and 2 of another kind.
1) Pick 1 denomination.
2) and then pick 3 cards.
3) and then pick 2nd denomination
4) and then pick 2 cards.
Find the number of ways to do each of the above. What do you do with each of those number
 

Dr.Peterson

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You should be aware that your problem is a little more complicated than Jomo's example, though his advice is exactly what I do.

Since you need at least 3 cards of the same suit, there may be exactly 3, 4, 5, or 6 of one suit. Unless you see a foolproof shortcut, I'd calculate each of those four cases separately. The first is perhaps the trickiest, because your count may double-count a case with three of one suit and three of another, since it would be counted for each of those two suits. The others should be easier, so maybe you should start with the easiest case: How many possible hands contain 6 cards of the same suit?
 
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