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You are not logged in. #1 20130324 23:28:49
Shared birthdaysWhat are the chances that 6 people celebrate their Birthday in the same 2 months? Assume all months are equal. Last edited by anna_gg (20130325 00:27:25) #2 20130325 00:09:04
Re: Shared birthdaysHi; Last edited by bobbym (20130325 00:13:40) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20130325 00:48:05
Re: Shared birthdaysHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20130329 10:24:04
Re: Shared birthdaysHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20130329 10:50:27
Re: Shared birthdaysHow'd you get that answer? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20130329 10:51:56
Re: Shared birthdaysHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20130329 10:56:02
Re: Shared birthdaysYes. I permuted the i and the e. It seems to be common with me. I have a tough time remembering whether it's Liebniz or Leibniz. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20130329 11:05:58
Re: Shared birthdaysNo, all combinatoric problems fall into categories. Surely you have read the 12 fold way or even better the 30 fold way. I have my own set in addition to those. These templates help solve many types of problems. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20130329 11:12:58
Re: Shared birthdaysWould you mind sharing? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20130329 11:20:55
Re: Shared birthdaysOf course you were half right I already had the answer before I even began. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20130329 11:23:54
Re: Shared birthdaysGreat, thank you! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20130329 11:33:13
Re: Shared birthdaysThis looks like some of Feller's work or maybe Rose, I am not sure. Surely you recognize that?! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20130329 21:54:19
Re: Shared birthdaysWhat the hell is that? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #16 20130329 22:18:03
Re: Shared birthdaysLooks like a formula! So you do not recognize it? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20130329 22:32:15
Re: Shared birthdaysIt looks like some stuff I've seen on Wiki's distributions pages. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #18 20130329 22:33:24
Re: Shared birthdaysBetter than that. With that you compute the answer to anna's problem quickly. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20130331 03:58:00
Re: Shared birthdaysI will try to share my solution in a more explanatory way (Sorry, Bobby, I don't imply that yours is not easy to understand  it is just that I am a novice and not very familiar with complicated solutions!!): Then we must calculate all the different ways by which we can arrange the birthdays of 6 people in these 2 months: Either 5 people have their birthday in the first month and 1 in the second, or 4 in the first and 2 in the second etc. Obviously we do not consider the case of 0/6 or 6/0. For the first case, we first get 1 out of 6 (for the first person’s birthday) and then for the second person’s it will be 5 out of 5, and so on. Here is the calculation: The total probability is the product of the first two (66 x 62) divided by the total number of all different ways by which 6 people can have their birthdays in 12 different months, that is, 12^6. So we have Last edited by anna_gg (20130331 03:58:57) #20 20130331 04:11:42
Re: Shared birthdaysHi anna_gg;
No problem. I am glad to see your solution. Also, anyone who can do that problem I do not characterize as a novice. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20130331 04:57:52
Re: Shared birthdaysNo I haven't; actually I wrote the solution in a Word doc, but when I copied it here, the formatting was screwed up ( #22 20130331 05:35:29
Re: Shared birthdaysHi anna_gg; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #24 20130331 07:04:32
Re: Shared birthdaysHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #25 20130331 09:35:21
Re: Shared birthdaysHm, then the solution for n people seems to be 66*(2^n2)/(12^6). The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 