Combinatorics

Prove that no of ways in which n identical objects can be dived in r different groups is: n+r-1 C r-1

(I did'nt get the prove of this in any of the books.)

9 Answers

62
Lokesh Verma ·

Try induction.. (The simplest solution :D)

take r=0 then start induction :P

I havent even read the question properly :D

11
sagnik sarkar ·

Please read it ,sir.
Can you try and prove that logically instead?

62
Lokesh Verma ·

oh yeah now i can read it too :)

see you have n 1's

now you have to put some r-1 + signs in between these 1's

so you have the proof?

3
msp ·

it was the same as

no of integral solutions for the eqn x0+x1+x2+.....+xn=r

62
Lokesh Verma ·

Yes sankara. you have recognised that well :)

except that you have replaced r and n?

3
msp ·

yes sir it damaged wat i meant :P

1
Philip Calvert ·

msp do you not recognize the proof bhaiyya has in mind ..
or was it simply that you are giving another method ..

3
msp ·

dude dat was by induction,i am searching for a combinatorial proof.Also i donno abt induction,

1
$ourav @@@ -- WILL Never give ·

nishant sir,plz give d induction proof....m not getting it....

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