# Combination Question



## xenou (Jan 25, 2013)

Maths problem:

Six cards are drawn from an ordinary deck of 52 cards.  How many ways is it possible to draw exactly 2 queens or kings?

The answer is (allegedly) 3,801,028 but how do you get to it?   I interpret exactly 2 queens or 2 kings to mean:

_2 queens and 4 other cards that are not queens.
_OR
_2 kings and 4 other cards that are not kings._

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I may be interpreting this wrong.  The answer I get is:

QUEENS: [6 ways to choose a pair] * [194,580 ways to choose the remaining four cards, excluding the queens] = 1,167,480, by which I mean (4 C 2) * (48 C 4) = 1,167,480
KINGS: Ditto

Added together: (4 C 2) * (48 C 4) * 2 = 2,334,960


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## taurean (Jan 26, 2013)

> Six cards are drawn from an ordinary deck of 52 cards.  How many ways is it possible to draw exactly 2 queens *or* kings?


If emphasis is put more on "or" then it could well mean:
2 cards are either queen or king i.e. any two cards out of 8 available.
Thus : COMBIN(8,2) = 28

And the rest is COMBIN(44,4) = 135751

Combined : 135751 * 28 = 3,801,028


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## xenou (Jan 26, 2013)

Excellent.  Thanks - that's it I think.
ξ


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