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Uniform distribution (Posted on 2019-01-25) Difficulty: 2 of 5
6 cards, labeled 1,2, ...6, are randomly put in 3 different envelopes, at least one card in each.

Evaluate the probability of 2,2,2 distribution.

No Solution Yet Submitted by Ady TZIDON    
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re(2): two different answers s.b. one | Comment 4 of 9 |
(In reply to re: two different answers s.b. one by Ady TZIDON)

Thank you sincerely Ady, for catching my typos. I have corrected my post. I give my replies to yours in order:

(In reply to two different answers by Steven Lord)

a.     5,2,0     s.b. 510     and   6!=120;  Please  redo your table.

Yes - I meant (and in fact I used 5,1,0) and now this is fixed. Thanks! And it is 3^6 = 729 = the total number of different ways to fill the envelopes.  Again, corrected - thanks!

b.       You should get the same answer i.e. 2/9

For the two cases I depicted, I think not. 

Suppose (this is my case #2): the the envelopes were stuffed and then someone noticed there was at least one card in each envelope. BTW, this one or-more card per envelope scenario happens 
[P(411)+P(321)+P(222)]/3^6 = 20/27 = 0.740740740... of the time. 

Then, the puzzle becomes a conditional probability question, I think:
p(222 | no zeroes) and my answer p=1/6 obtains. 

c.  DISTINCT cards or IDENTICAL cards should yield the same result.

Exactly. That was my joke, right?  There's no point in mentioning that the cards were numbered, right?  You see, I am light-hearted about these puzzles - if they are not fun, then why do them (aside from staving-off senility)?

With my best regards for giving us so many fun puzzles -  Steve

Edited on January 26, 2019, 4:29 am
  Posted by Steven Lord on 2019-01-26 04:20:02

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