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 $4^5$.
In how many ways $5$ different rings can be worn on $4$ fingers ?   Although these is similar question here   But I want to answer it in different way which is like take $4$ fingers like $a,b,c,d$. Now $a$ can be filled in $5$ ways and so are others. So total ways are $5^4$ but answer is $4^5$. What is wrong in my reasoning? Which cases have I left out?
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