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.

https://www.meritnation.com/ask-answer/question/prove-npr-n-n-r-and-deduce-it-t/binomial-theorem/3191087

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 

 

Now,

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

 

 

  • -17
What are you looking for?