Confused about a card question

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GabeFried

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The game of euchre uses only the 9s, 10s, jacks, queens, kings and aces from a standard deck of cards.
How many different 4-card hands could have at least one card from each suit?
Thanks in advanced :)
 
GabeFried said:
The game of euchre uses only the 9s, 10s, jacks, queens, kings and aces from a standard deck of cards.
How many different 4-card hands could have at least one card from each suit?
Thanks in advanced :)
Click to expand...
in this game

how many cards are used for each round?
 
It looks like there are 24 unique cards (6x4) in a euchre deck.

Thus there will be (24 choose 4) different hands. [edited]

I leave you to compute that number.
 
Last edited by a moderator:
Romsek said:
It looks like there are 24 unique cards (6x4) in a euchre deck.

Thus there will be (24 choose 4) different hands.

I leave you to compute that number.
Click to expand...
First card can be chosen 24 ways.

Now we have to discard the suit of the first card.

second card can be chosen 18 ways.

continue ..
 
Romsek said:
It looks like there are 24 unique cards (6x4) in a euchre deck.

Thus there will be (24 choose 4) different hands.

I leave you to compute that number.
Click to expand...

oops I didn't catch part of the question. Ignore the above.
 
GabeFried said:
The game of euchre uses only the 9s, 10s, jacks, queens, kings and aces from a standard deck of cards. How many different 4-card hands could have at least one card from each suit?Thanks in advanced
Click to expand...
You have posed a game of cards from a standard deck. It consists of six denominations and the four standard suits.
With that understanding, your question is "How many different 4-card hands could have at least one card from each suit?"
Answer: \(\dbinom{6}{1}^4=6^4\) That is selecting one card from each of four suits consisting six denominations.
 
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