From Statistical Inference Second Edition (George Casella, Roger L. Berger)
"My telephone rings 12 times each week, the calls being randomly distributed among the 7 days. What is the probability that I get a least one call each day?"
The answer is .2285, but I don't know how they got it. My reasoning was as follows:
There are 12 calls and thus 13 places to put "day dividers" to produce possible distributions of calls. There should be 6 day dividers for the week. One possibility:
(1 on Monday, 2 on Tuesday, 3 on Wednesday, 1 on Thursday, 1 on Friday, 0 on Saturday, 4 on Sunday)
13^6 possible distributions (using this method). In order to satisfy 1 call/day, dividers can't be at the beginning or end, nor can they be on top of one another (signifying a day with no calls). This means there are:
Valid distributions and a probability of: 0.069. Where am I going wrong?
(P.S. This isn't homework as I'm not in school.)
Edit: I don't think each "distribution" is equally likely. That's probably my error. But I still don't know how to get to the correct answer :)