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Consider a deck of cards:

How many different 4-card hands can have each card from a different suit?

User AndrewKS
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1 Answer

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Ohhhh nasty ! What a delightful little problem !

The first card can be any one of the 52 in the deck. For each one ...
The second card can be any one of the 39 in the other 3 suits. For each one ...
The third card can be any one of the 26 in the other 2 suits. For each one ...
The fourth card can be any one of the 13 in the last suit.

Total possible ways to draw them = (52 x 39 x 26 x 13) = 685,464 ways.

But wait ! That's not the answer yet.

Once you have the 4 cards in your hand, you can arrange them
in (4 x 3 x 2 x 1) = 24 different arrangements. That tells you that
the same hand could have been drawn in 24 different ways. So
the number of different 4-card hands is only ...

(685,464) / (24) = 28,561 hands.

I love it !


User ICoffeeConsumer
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