What is the coefficient ofp^8q^3 ?
1 Answer
Mar 9, 2018
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#