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?

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Total no. of things=n

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

âˆ´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.

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