How to find number of injections from a finite set A to finite set B where |A| < |B|?

Question

I need to find number of injections from a finite set A to finite set B where |A| < |B|. How could i do that? I don't understand what does |A| and |B| mean

Answer 1

$|A|$ means the cardinality of set $A$. We have $|B|$ options for the first element of $A$, $|B|-1$ options after that for the second element and so on (if we want to make this an injection), so the number of injections is $$|B|(|B|-1)\cdots(|B|-|A|+1)=\frac{|B|!}{(|B|-|A|)!}$$