Problems from Variations with repetition

In the football pools of $$15$$ matches, it is possible to mark the result of every match with $$1$$, $$X$$ or $$2$$. In how many ways is it possible to realize the football pools?

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Development:

In this case, $$n=3$$ (because it is possible only to choose for every match either $$1$$, or $$X$$ or $$2$$), and $$k = 15$$ (because in total there are $$15$$ matches). Also, the order matters.

On the other hand, elements can be repeated (it is possible to mark more than one match with a $$X$$, for example). Therefore it is a question of varying the repetitions of $$3$$ elements from $$15$$ by $$15$$, that is to say: $$$PR_{3,15}=3^{15}=14.348.907$$$

Solution:

There are $$14.348.907$$ possible football pools (which indicates that there is very little possibility of winning!)

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