H2 Math - Permutations & Combinations

Prove the following statement.

(n choose r) = ( (n-1) choose (r-1)) + ((n-1) choose r)

where r and n are positive integers such that r is less than or equal to n using

(i) and algebraic argument

(ii) a combinatiorial argument [ Hint: consider choosing r objects from n distinct objects]

Thanks

Hi,

(i) Consider the fact that nCr = n! / { r! (n - r)! }.

(ii) Please read this: http://www.math.uvic.ca/faculty/gmacgill/guide/combargs.pdf

Thanks.

Cheers,
Wen Shih