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Fundamental Principle of Counting

In a steamer ...

Question

In a steamer there are stalls for $12$ animals, and there are cows, horses, and calves (not less than $12$ of each) ready to be shipped; in how many ways can the shipload be made?

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Solution

$⟹$ The number of arrangements of $n$ things (each consisting a valid amount ) into $r$ things is $n^{r}$
$∴ 3$ animals arranged over $12$ stalls in $3^{12}$ ways
i.e. $531441$ no. of ways.

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