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# Combinatorics Problem

There are $$n$$ types of different articles. The names of the types are - $$A_1,A_2,A_3,...,A_n$$ Number of article $$A_1$$ is $$N_1$$ , $$A_2$$ is $$B_2$$... same goes upto $$A_n$$. We have to choose k articles.Repetition is allowed.

Note by Soham Chanda
4 years, 6 months ago

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Can't understand · 4 years, 6 months ago

Comment deleted Feb 22, 2013

I think that formula can only be used when we are permuting all the objects given. When there is a limit of k objects as imposed in the question, I don't think it can be used. The answer will not be right.

That having been said, we can apply the Multinomial Theorem to find the answer. A question based on this Theorem is posted here. https://brilliant.org/discussions/thread/integer-partitions/ · 4 years, 6 months ago

Can you show the steps? · 4 years, 6 months ago

This link has a specific case of the question you have asked. In this case, when you have to create a limited length word, you cannot use the Mississippi formula. On Yahoo Answers, the asker says that the Mississippi formula does not work. The answer given will not be easy to derive for a specific case. The Multinomial Theorem works better there. I will upload a detailed solution soon. · 4 years, 6 months ago

I know that process but that's SO tedious.Wanted a generalization. · 4 years, 6 months ago

It is easier to choose the k objects, as required in this question you posted, than it is to permute the objects, as you would have to do for the Yahoo Answers case. With respect to your question, I have a Multinomial Theorem answer, but it is too long to type out. If only I could upload a picture... · 4 years, 6 months ago

you can start a new discussion where you can upload the picture..i'd really appreciate it · 4 years, 6 months ago