# 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 \(a_i \neq i\) ?