Henry Ernest Dudeney/Modern Puzzles/64 - Dividing by Eleven

by : $64$

 * Dividing by Eleven
 * If the $9$ digits are written at haphazard in any order,
 * for example $4 \ 1 \ 2 \ 5 \ 3 \ 9 \ 7 \ 6 \ 8$, what are the chances that the number that happens to be produced will be divisible by $11$ without remainder?
 * The number I have written at random is not, I see, so divisible, but if I had happened to make the $1$ and the $8$ change places it would be.