ELMO SL 2012 N4

Do there exist positive integers $b,n>1$ such that when $n$ is expressed in base $b$ , there are more than $n$ distinct permutations of its digits? For example, when $b=4$ and $n=18$ , $18 = 102_4$ , but $102$ only has $6$ digit arrangements. (Leading zeros are allowed in the permutations.)

Lewis Chen.