(a)     Find the value of $n$ .

(b)     Hence, find the coefficient of ${x^2}$ .

(a)     coefficient of ${x^3}$ is $\left( {\begin{array}{*{20}{c}}   n \\   3 \end{array}} \right){\left( {\frac{1}{2}} \right)^3} = 70$     M1(A1)

$\frac{{n!}}{{3!\left( {n - 3} \right)!}} \times \frac{1}{8} = 70$     (A1)

$\Rightarrow \frac{{n\left( {n - 1} \right)\left( {n - 2} \right)}}{{48}} = 70$     (M1)

$n = 16$     A1

(b)     $\left( {\begin{array}{*{20}{c}}   {16} \\   2 \end{array}} \right){\left( {\frac{1}{2}} \right)^2} = 30$     A1

[6 marks]

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