Let $n$ be a positive integer.

(a) There are $n^2$ ordered pairs $(a,b)$ of positive integers, where $1 \le a,$ $b \le n.$ Using a counting argument, show that this number is also equal to
\[n + 2 \binom{n}{2}.\]
(b) There are $n^3$ ordered triples $(a,b,c)$ of positive integers, where $1 \le a,$ $b,$ $c \le n.$ Using a counting argument, show that this number is also equal to
\[n + 3n(n - 1) + 6 \binom{n}{3}.\]