combi
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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Re: combi
$\frac{\binom{3}{1}\cdot\frac{5!}{3!}+\binom{3}{2}\cdot\frac{5!}{2!\cdot2!}}{3^5}$
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Re: combi
গুণের জন্য \cdot দাও, তোমারটা দশমিক মনে হয়...
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Re: combi
i'm explaining it's numerator...
there should be one of each letter A, B, C... then we need 2 more letters... these 2 letters can be different or same...
one kind of letter(for 2 same letters) can be chosen in $\binom{3}{1}$ ways... then we can arrange 5 letters in $\frac{5!}{3!}$ ways, as there are 3 same letters in each choice(considering previous A, B, C also)...
2 different letters can be chosen in $\binom{3}{2}$ ways... then we can arrange 5 letters in $\frac{5!}{2!\cdot2!}$ ways, as there are 2 same letters twice in each choice...
there should be one of each letter A, B, C... then we need 2 more letters... these 2 letters can be different or same...
one kind of letter(for 2 same letters) can be chosen in $\binom{3}{1}$ ways... then we can arrange 5 letters in $\frac{5!}{3!}$ ways, as there are 3 same letters in each choice(considering previous A, B, C also)...
2 different letters can be chosen in $\binom{3}{2}$ ways... then we can arrange 5 letters in $\frac{5!}{2!\cdot2!}$ ways, as there are 2 same letters twice in each choice...
Re: combi
Bonji, tomar ki mone hoi na tumi aktu complicated hishab korteso!!
btw tomar oi soln purna sonkhai ashtese to??? ami calc dia fraction paitesi kan??
btw tomar oi soln purna sonkhai ashtese to??? ami calc dia fraction paitesi kan??
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: combi
btw, tushar er songe amar sol'n mile! :p
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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Re: combi
you should consider repetition... i solved it with 2 steps for counting permutations with repetition...labbi wrote:tomar ki mone hoi na tumi aktu complicated hishab korteso!!
probability can be fraction...ami calc dia fraction paitesi kan??
Re: combi
Tushar, please explain how you have got $\frac{6\cdot3^2}{3^5}$ ? May be you have done some mistakes
আর আমার সামান্য confusion আছে। শব্দগুলা কি খালি A,B,C দিয়ে তৈরি নাকি এর বাইরের অক্ষর ব্যবহার করা যাবে? যদি না যায় তাহলে জান্নাতের সমাধান ঠিক আছে।
আর আমার সামান্য confusion আছে। শব্দগুলা কি খালি A,B,C দিয়ে তৈরি নাকি এর বাইরের অক্ষর ব্যবহার করা যাবে? যদি না যায় তাহলে জান্নাতের সমাধান ঠিক আছে।
Every logical solution to a problem has its own beauty.
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(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)