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?
See development and solution
Development:
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: $$$V_{15,5}=\dfrac{15!}{(15-5)!}=360.360$$$
Solution:
In conclusion, the child can say $$360.360$$ phrases (of course, not all of them make sense!)