Understanding a special combination

[anigeo]

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.

 

[mathman]

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.

 

[anigeo]

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.

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?

 

[mathman]

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".

 

[anigeo]

that's the thing, u got it.but how can u say that it can be dealt in only 2 ways?

 

[mathman]

that's the thing, u got it.but how can u say that it can be dealt in only 2 ways?

That's what it is to prove the particular equation. If it's more than two ways, you have a different expression.