H2 Math - Permutations & Combinations

• Audi

  25 Apr 12, 23:05

  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

• wee_ws

  26 Apr 12, 08:04

  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