Let $A,B$ be groups such that $\left | A \right | = 7$ $\left | B \right | = 5$ and let $a\in A$ and $b\in B$
Find the number of onto functions $f:A \mapsto B$ where $f(a) = b$
Using the inclusion - exclusion principle I found that all the surjective functions from $A$ to $B$ is $16,800$
My question is, should I treat somehow that $f(a) = b$ for $a\in A$ and $b\in B$?
Does it change the way I treat the question somehow? thanks.