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 Three of a Kind (Posted on 2003-11-19)
You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?

You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)

 No Solution Yet Submitted by Lewis Rating: 4.3333 (9 votes)

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 One flaw in your reasoning... | Comment 29 of 39 |
(In reply to When you're right, you're right, SilverKnight... by Dan)

Dan,

I think you're just throwin' these up in the air for me to slam down like a volleyball....

You wrote:
"Let me break this out. The 52*51*50*49*48=51979200 part is correct if duplicates are not eliminated." ... "I defy anyone to find a flaw in that reasoning."

Well... according to my calculations...

52*51*50*49* 8 = 51979200

so... I if we replace the 8 with a 48...
we get 311,875,200

Then, you suggested we multiply:
(4*3*2)*(48*46)*(10) = 529920
But I wonder... if we replace the 46 with a 44:
we get 506,880

Now 506880/311875200 = .0016252655

Hmmm.... that number sure looks familiar... wait... I saw it somewhere.... yes! I remember now... it was in a couple of my earlier comments.

 Posted by SilverKnight on 2003-11-20 21:57:52

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