SOLUTION: please help me solve this binomial expansiom show that the coefficient of {{{a^12b^3}}} in a binomial expansion of {{{(a+b)^15}}} is 455. use the the expansion to evaluate{{

Question 1104285: please help me solve this binomial expansiom

show that the coefficient of in a binomial expansion of is 455. use the the expansion to evaluate

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
show that the coefficient of in a binomial expansion of is 455. use the the expansion to evaluate
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a^12*b^3 is in the term (15C12)a^12b^(15-12)
with coefficient 15C12 = 15!/[(15-12)!*12!] which equals 455
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1.02^15 = (1+02)^15 = 15C15*1^15*0.02^0 + 15C14*1^14*0.02^1 + 15C13*1^13*0.02^2 +....+ 15C0*1^0*0.02^15
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1.02^15 = 1*1*1 + 15*1*0.02 + [(15*14)/(1*2)]*1*0.02^2 + ...+ 1*1*3.2768x10^-26
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= 1.34586...
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Cheers,
Stan H.
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