How can we prove the formula n+r-1Cr when r things are to be selected out of n type of things where each object may be repeated any no. of times? OR how can we justify this formula logically?

Here is the link similar to your query.

Total no. of things=n

no. of items chosen from total no. of things =r

∴There are n ways of replacing the first object and for second , there are (n-1) ways and 

for rth ,there are  (n-r+1) ways.

Thus, the total number  for the order to be relevant is 



No. of ways to rearrange the group = r! ways.



  • -17
What are you looking for?