The total number of onto functions from the set $\{1, 2, 3, 4\}$ to the set $\{3, 4,7\}$ is ______.

If A and B are two sets consisting of m and n elements respectively such that $1 ≤ n ≤m$, then number of onto functions from A to B is

$\sum\limits_{r=1}^{n}(-1)^{n-r}\,{^nC}_r\,r^m$

Here, m = 4 and n = 3.

So, total number of onto functions

$=\sum\limits_{r=1}^{3}(-1)^{3-r}\,{^3C}_r\,r^4$

$={^3C}_1-{^3C}_2×2^4+{^3C}_3×3^4=3-48+81=36$