Combination Question

[xenou]

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

 

[taurean]

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

 

[xenou]

Excellent. Thanks - that's it I think.
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