Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding a special combination

  1. Oct 20, 2011 #1
    nC0+nC1+nC2+..................+nCn=2^n

    in the analytic proof for this my books say that it is the total number of combinations of n different things taken at least 1 at a time.
    they say that each object can be dealt in 2 ways, either it can be accepted or it can be rejected.
    hence n objects can be dealt in 2^n ways.
    but how in selection how does the question of rejection come?what is the significance of this rejection?please explain.
     
  2. jcsd
  3. Oct 20, 2011 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    I can't understand your question. However a simple proof of the equation is by means of the binomial theorem. Expand (a+b)n and then let a=b=1 and you will get the result.
     
  4. Oct 20, 2011 #3
    the binomial proof is done.this is the analytic proof in which they say that every object of n objects can be dealt in 2 ways,s objects can be dealt with in 2^2 ways,3 in 2^3 ways.this includes an acceptance of the object or its rejection.acceptance or selection is all right.how does the question of rejection arise?
     
  5. Oct 21, 2011 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    It looks to be a matter of wording. Since every object can be dealt with in either of two ways, the two ways may be labeled "acceptance" or "rejection".
     
  6. Oct 21, 2011 #5
    that's the thing, u got it.but how can u say that it can be dealt in only 2 ways?
     
  7. Oct 22, 2011 #6

    mathman

    User Avatar
    Science Advisor
    Gold Member

    That's what it is to prove the particular equation. If it's more than two ways, you have a different expression.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Understanding a special combination
  1. Possible Combinations (Replies: 5)

  2. Combinations Problem (Replies: 4)

  3. Combination question (Replies: 6)

  4. Combination of cards (Replies: 16)

  5. Booze combinations (Replies: 12)

Loading...