$($a$)$ Find an injective map $$:$52^3,$ where we think of $5$ as the five

element set $\{0,1,2,3,4\}$ and $2^3$ as the eight element set $\{0,1{\}}^3,$ the

set of binary strings of length $3.$

$($b$)$ Using the map $$ from the previous part, define an injective map

$f$:$5^N{2}^N$

$($c$)$ Show that $5^N$ and $2^N$ have the same cardinality.