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: Prove that nCk is a natural number

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that [tex]\binom{n}{k}[/tex] is a natural number by showing that [tex]\binom{n}{k}[/tex] is the number of sets of exactly [tex]k[/tex] integers each chosen from [tex]1, ..., n[/tex].

    2. Relevant equations

    3. The attempt at a solution

    I posted a similar question before (https://www.physicsforums.com/showthread.php?t=339363) which asked for a proof by induction. This question is a bit different, and I'm not entirely sure how to get started. I'd appreciate some hints. Thanks.
  2. jcsd
  3. Oct 24, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Here's your hint. How many different sequences (ordered!) of integers can you pick from the set {1,...,n}? Count sequences. Mull over that for a bit.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook