nCr= n-1Cr + n-1Cr-1 is a famous recursive equation for computing nCr , where nCr means number of ways selecting r objects from n objects.

I have read in high school the logical meaning of this formula.

I remember my teacher saying that to calculate number of ways of selecting r objects from n objects(nCr) , we can either discard object at r postion(i.e n-1Cr-1) , or we can include the object at r position (i.e n-1Cr).but I don’t understand this logic now …!! can someone plz explain me this with some example or any editorial…??

Thank you.

@va1ts7_100 It can be understood as, suppose you want to select a group of * r* students out of

*students, which can be done in \binom{N}{r} ways. Then, for each student there are two possibilities that either it would be selected in that group of*

**N***students or it will be rejected. Let, out of these*

**r***students there is a student*

**N***which will either be selected in group of those*

**’A’***students or won’t be selected. If you select*

**r***in the group then you have total*

**A***students left and you have to select remaining*

**N-1***students, which can be done in \binom{N-1}{r-1} ways, and if you don’t select*

**r-1***then you have total*

**’A’***students left and you have to select*

**N-1***students from it which can be done in \binom{N-1}{r}. So, the total number of ways of selecting*

**r***students out of*

**r***students is equal to \binom{N-1}{r} + \binom{N-1}{r-1}.*

**N**good explanation… lucid … thanks

Really, wonderful explanation. Thank you very much, bro.

Amazing explanation! Thank you.