Number of onto functions from A to B if n(A)=6 and n(B)=3 is

No. of surjective functions if $n(A)=m$ and $n(B)=n$

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

$=\sum\limits_1^3(-1)^{3-r}{^3C}_r×r^6$

$=({^3C}_1×1^6)-({^3C}_2×2^6)+({^3C}_3×3^6)$

$=540$