Injective Function Combinations

Question

If $|A| = 5$ and $ |B| =25$ , how many functions from $A$ to $B$ are injective?

I'm not quite sure how to tackle this problem as I do not quite understand what $|A| = 5$ and $|B| = 25$ means .

Answer 1

The number of injective maps from $A$ to $B$ is $n!\times \binom{m}{n}$ with $m = |B|, n = |A|$. In your case, it's $5!\times \binom{25}{5}$.

Answer 2

To each elements in A, we associate a unique elements in B, there are $25$ choices for what $1$ gets map to, then $24$ choice for what $2$ gets map to and so on. So $25*24*23*22*21=6 375 600$.