# Letters & Envelopes

THUDandBLUNDER
Posers and Puzzles 16 Jun '04 14:16
1. 16 Jun '04 14:16
You have four addressed letters and four addressed envelopes. If you close your eyes and randomly insert letters into envelopes, what is the probability that exactly three letters will be in the right envelopes?

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2. bbarr
Chief Justice
16 Jun '04 14:271 edit
Originally posted by THUDandBLUNDER
You have four addressed letters and four addressed envelopes. If you close your eyes and randomly insert letters into envelopes, what is the probability that exactly three letters will be in the right envelopes?

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1/4 X 1/3 X 1/2 = 1/24

3. 16 Jun '04 14:31
Originally posted by bbarr
1/4 X 1/3 X 1/2 = 1/24
Nope.
4. bbarr
Chief Justice
16 Jun '04 14:59
Originally posted by THUDandBLUNDER
Nope.
Tricky. The probability is 0. If three are correct then the fourth must be also. Of course, the probability I gave above was for randomly placing all four envelopes correctly.
5. Coletti
W.P. Extraordinaire
17 Jun '04 01:32
Originally posted by bbarr
Tricky. The probability is 0. If three are correct then the fourth must be also. Of course, the probability I gave above was for randomly placing all four envelopes correctly.
Cool! I think you're right bbarr, the answer is zero for the reason you stated. And I was going to add that THUDandBLUNDER should have stated that only one letter should go into any one envelope, but that would given to big a clue to the solution and made it too easy.
6. 17 Jun '04 17:10
Im pretty sure it's not zero, because it is possible for it to happen. I can't remember the equation off hand, but it's not quite 4! - I'll consult my communications book -
7. Otis
Lucky Patzer
18 Jun '04 06:51
what if i stuffed 3 letters in the correct envelopes and then stuffed the extra letter with another letter leaving an envelop empty then there could be 3 correct and 1 false
8. 18 Jun '04 08:191 edit
Originally posted by Otis
what if i stuffed 3 letters in the correct envelopes and then stuffed the extra letter with another letter leaving an envelop empty then there could be 3 correct and 1 false
Perhaps I should have made it clear that one and only one letter goes into each envelope, in which case the right answer is zero.

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9. Otis
Lucky Patzer
18 Jun '04 08:22
0 because you have no hands duh
10. 19 Jun '04 08:23
well if you only stuff 3 of the envelopes with letters, then what is the probability?
11. 19 Jun '04 11:181 edit
Originally posted by Awry
well if you only stuff 3 of the envelopes with letters, then what is the probability?
Probability = (1/4)(1/3)(1/2) = 1/24

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