The number of strictly increasing functions $f$ from the set ${1,2,3,4,5,6}$ to the set ${1,2,3,\ldots,9}$ such that $f(i) \ne i$ for $1 \le i \le 6$, is equal to:

$f(i) \ne i$, $f(x)$ is strictly increasing function

$f : A \to B$, where $A = {1,2,3,4,5,6}$

$B = {1,2,3,\ldots,9}$

$f : A \to B$ is equal to

Case–i: $f(1) = 2 \Rightarrow {}^7C_5 = 21$

Case–ii: $f(1) = 3 \Rightarrow {}^6C_5 = 6$

Case–iii: $f(1) = 4 \Rightarrow {}^5C_5 = 1$

No of function $A$ to $B = 21 + 6 + 1 = 28$