1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Binomial coefficients and pascal's triangle

  1. Aug 20, 2005 #1
    I am working through a mathematics olympiad problem book, and I am asked to prove that n choose r, where n is the row number and r is the term number in the row is equal to that term. Can someone please give me a hint? I have not been able to find ANY proofs on the internet through a basic search, just sites that acknowledge the relationship between binomial coefficients/theorem and pascal's triangle.
     
  2. jcsd
  3. Aug 20, 2005 #2

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    It might help to recognize that each number in Pascal's triangle is equal to the total number of ways of reaching that location starting at the top and moving downward such that in going from one row to the next you can only move one step to the left or one step to the right. (Like a random walk!)
     
  4. Aug 20, 2005 #3

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Here's another way to do it:

    Find some algebraic conditions that completely specify Pascal's triangle.
    Prove that nCr satisfies those algebraic conditions.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Binomial coefficients pascal's Date
BInomial distribution Sep 11, 2017
Need help in applying Binomial Aproximation when y L? Mar 21, 2015
Gravitation and Binomial Expansion Oct 28, 2014
Binomial Coefficients Sep 21, 2005
Binomial Coefficient problem Jan 14, 2005