Question

How to prove nCr + nCr-1 = n+1 Cr Explain me in simple and explained manner Experts... I will be waiting....

Answer 1

hi Avaneesh,

Always remember :::    nCr = n! / (n-r)! * r!   and   r! = r*(r-1)!

nCr
= n! / (n-r)! * r!
= n! / (n-r)! * r(r-1)!

nCr-1
= n! / (n-(r-1))! * (r-1)!
= n! / (n-r+1)! * (r-1)!
= n! / (n-r+1)(n-r)! * (r-1)!

(n+1)Cr
= (n+1)! / ((n+1) - r)! * r!
= (n+1)n! / (n-r+1)! * r(r-1)!

now
LHS
= nCr + (n+1)Cr
= n! / (n-r)! * r(r-1)!    +   n! / (n-r+1)(n-r)! * (r-1)!
= n! (  (n-r+1) + r  / (n-r+1)(n-r)!*r(r-1)!   )
= n!  ( n-r+1-r  /  (n+1 - r)(n-r)! * r! )
= n! ( n+1 /  ((n+1) - r)! * r! )
= (n+1)n! / ((n+1) -r)! * r!
= (n+1)! / ( (n+1) -r )! * r!
= (n+1) C r
= RHS

Hope it helped
Let me know if any doubts
Cheers !!!

Answer 2

Answer:

Step-by-step explanation:

Answer is attached below