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

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

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