In how many ways can $3$ different rings be worn on $4$ fingers with at most one on each finger?
[Math] In how many ways $3$ different rings can be worn in $4$ fingers with at most one in each finger
combinatorics
combinatorics
In how many ways can $3$ different rings be worn on $4$ fingers with at most one on each finger?
Best Answer
$24+3\cdot 12+3\cdot 4+1=73$
Two ways to think about it: (m is max # of rings, n is # of fingers, k is # of used rings)
$$\sum\limits_{k=0}^m\binom{m}{k}\frac{n!}{(n-k)!}=\sum\limits_{k=0}^m\binom{n}{k}\frac{m!}{(m-k)!}$$