What is the coefficient ofp^8q^3 ?

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1 Answer
Jim G.
Mar 9, 2018

#165#

Explanation:

#"using the "color(blue)"Binomial theorem"#

#•color(white)(x)(p+q)^n=sum_(r=0)^n((n),(r))p^((n-r))q^r#

#"where "((n),(r))=(n!)/(r!(n-r)!)#

#"and "n! =n(n-1)(n-2).......xx3xx2xx1#

#"here we require "color(blue)(r=3)#

#rArrT_(n+1)=((11),(3))p^((11-3))q^3=((11),(3))p^8q^3#

#"coefficient of "p^8q^3=((11),(3))#

#((11),(3))=(11!)/(3!xx8!)#

#color(white)(xxxxxx)=(11xx10xx9xxcancel(color(red)(8!)))/(3xx2xx1xxcancel(color(red)(8!))#

#=(11xx10xx9)/6=165#

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