Binomial Coefficients : The coefficient of a^10 b^4 and the coefficient of a^6 b^8

In the expansion (a+b)^14 find:
a) The coefficient of a^10 b^4.
b) The coefficient of a^6 b^8.


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Definition of Binomial Coefficient:

Given a set X and a non-negative integer r, an r-subset of X is a subset A  X of cardinality r.  We denote the set of r-subsets of X by Pr(X), i.e.
Pr(X) = {A  X | |A| = r}.

We define the binomial coefficient or binomial number ( n,      
                              r)
(read 'n choose r') to be the  cardinality of the set Pr(X) when
|X| = n.

The binomial Theorem:

For all real numbers a and b and non-negative integers n,
(a+b)n =   n      
    Sum  (n,    a(n-i) b(i)
     i=0      i)

     =  an + …+ (n,  a(n-i) b (i) +…..+ bn  .  
  i)

Problem:
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Attached file(s):

Prob2.doc  View File