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?)

(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.