How many strictly increasing functions $[4]\to [12]$ precede (2,3,4,5)?

I'm having some trouble with the following question:

Notation: Let [n] denote the set $\{1,...,n\}$ and we will represent a function $[k]\to [n]$ as a list: $(f(1),f(2),...,f(k))$

Consider all strictly increasing functions $[4]\to [14]$ and order them with the natural lexicographic order induced by the order in [14]. How many functions precede the function (2,3,4,5)?

- $(}\genfrac{}{}{0ex}{}{13}{4}{\textstyle )$

$(}\genfrac{}{}{0ex}{}{13}{3}{\textstyle )$

$(}\genfrac{}{}{0ex}{}{15}{3}{\textstyle )$

$(}\genfrac{}{}{0ex}{}{14}{3}{\textstyle )$