# Total number of increasing functions

Discrete Mathematics Level 5

How many increasing functions $$f$$ are possible such that $$f:A \rightarrow B$$, where $$A=\{ a_1,a_2,a_3,a_4,a_5,a_6\}$$ , and $$B=\{ 1,2,3,4,5,6,7,8,9\}$$ and $$a_{i+1}>a_i \forall i \in \mathbb{N}$$ and $$a_i \neq i$$ ?

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