In the expansion of ${{\left( 1-2b \right)}^{n}}$ in ascending powers of $b$, the coefficient of the third term is $112$.
(a)
Find the value of $n$.
(b)
Without writing the expansion of ${{\left( 1-2b \right)}^{n}}$, explain why the coefficient of the ${{\left( r+1 \right)}^{\text{th}}}$ term is an even number.
(a)
(b)