# Total number of increasing functions

Probability Level 5

How many strictly 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 $f( a_i) \neq i$ ?

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