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Theory of counting question

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tantoun2004

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Q:How many possible arrangments can be done with n objects taken r times with repetition and unordered (i.e.: order is not important we count differnt combinations of same elemnts as one like the usual combinations)
ANS: C(n+r-1,r)
where C is combination i.e. as if the problem was to deal with n+r-1 objects taken r times without repetition and unordered
This can be found in many books without proof. I tried to make a logical physical link between the 2 cases but I couldn't -> How to transform from a case in which we don't allow repetition to another with repetition.
Can anyone help?
 

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