I'm doing Permutations and Combinations and I'm facing difficulty with Permutations with repetitions. My book states that if there are $n$ objects chosen $r$ at a time, the total number of permutations is $n^r$.
I cannot understand how to decide what $n$ is and what $r$
In the following problem:
In how many ways can 6 different rings be worn on 4 fingers?
While I can solve this using the Multiplication Principle, I keep thinking that $n$ is the number of rings (as in my textbook it says that there are '$n$' different things') and $r$ is the number of fingers.
Best Answer
It is reasonable to suppose that the order of rings on fingers matters. Blue then white then red on the ring finger looks better than red then blue then white.
To count the number of ways to choose the number of rings the various fingers will hold, use Stars and Bars. The number of choices is $\binom{9}{3}$. For each choice, the rings can be permuted in $6!$ ways, for a total of $\binom{9}{3}6!$.