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Consider functions $f:\{1,2,3,4,5\} \to \{0,1,2,\ldots,9\}\text{.}$

How many of these functions are strictly increasing? Explain. (A function is strictly increasing provided if $a \lt b\text{,}$ then $f(a) \lt f(b)\text{.}$ )

How many of the functions are non-decreasing? Explain. (A function is non-decreasing provided if $a \lt b\text{,}$ then $f(a) \le f(b)\text{.}$ )