In how many ways can $5$ rings of different types be worn on $4$ fingers?

Question

In how many ways can $5$ rings of different types be worn on $4$ fingers?

According to me,first finger have $5$ ways,second finger have $4$ ways, third finger have $3$ ways and last finger have $2$ ways.

Therefore there are $5 \cdot 4 \cdot 3 \cdot 2 = 120$ arrangements.

But in my textbook it's answer is $4^5$.

Answer 1

Your textbook goes for: "each of the $5$ rings has a choice out of $4$ fingers."

Answer 2

This question is not well stated. This question doesn't shows information about the limitation of number of ring on a particular finger. According to you it's limitation is 1 but in your book it doesn't have limitation.

Answer 3

Assuming the order of rings on each finger is not important, you can look at the problem in the following way: take the first ring, you have 4 options (fingers) for it, right? Next ring, you have the same number of options, so it is $4 \times 4 = 4^2$, and so on. For 5 rings it is obviously $4^5$.