Find the probability that if each of the digits 0, 1, 2, ..., 9 be placed exactly once in random order in the blank spaces of:

5_383_8_2_936_5_8_203_9_3_76

the resulting number will be divisible by 396.

(In reply to

re: spoiler, hopefully by Math Man)

I wrote:

REM: unless I've erred in my hasty **addition.**

I've checked my **addition** twice, but not the subtraction, my

result was 1 instead of 11.

I must admit that it was immediately clear that only divisibility by

11 mattersl and that the final result must be either zero or 1, since adding 45 ( to even places only) is independent of the addends

distribution.

**Mea culpa**.