Problems from Variations without repetition

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: $$V_{15,5}={\displaystyle \frac{15!}{(15-5)!}}=360.360$$

Solution:

In conclusion, the child can say $360.360$ phrases (of course, not all of them make sense!)

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