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Variations without repetition
A small child knows $15$ words. Also, he can only say $5$ followed words in a row. How many phrases of $5$ (different) words is he capable of saying?
The child can only say $15$ words, that is to say $n=15$.
On the other hand, the phrases are $5$ words, that is to say $k=5$. Since the order of the words in a phrase matters (it is not the same to say "The child wants the dog" that "The dog wants the child") and the words cannot be repeated, it is a question of varying $15$ elements when we take five at a time.
Therefore we see that: $$V_{15,5}=\dfrac{15!}{(15-5)!}=360.360$$
In conclusion, the child can say $360.360$ phrases (of course, not all of them make sense!)