Let S be the set of all 5-digit numbers that contain the digits $1,3,5,7$ and 9 exactly once (in usual base 10 representation). Show that the sum of all elements of S is divisible by 11111. Find this sum.
Let S be the set of all 5-digit numbers that contain the digits $1,3,5,7$ and 9 exactly once (in usual base 10 representation). Show that the sum of all elements of S is divisible by 11111. Find this sum.