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: $P R_{3, 15} = 3^{15} = 14.348 .907$

Solution:

There are $14.348 .907$ possible football pools (which indicates that there is very little possibility of winning!)

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