[M.B.E.]

If you have only the digits 0, 1, and 5 to work with, you can form 177,147 eleven-digit numbers. That is just 3^11. For each of the eleven digits you have three choices (0, 1, or 5), so you just multiply together the eleven 3s.

If you assume that every ESN from 00000000000 to 99999999999 is equally likely, then the probability that an ESN contains no digits other than 0, 1, and 5 is

177,147/(10^11) = 0.00000177147 = 1/564,503

That's equal to (3/10)^11, which is what MrBlini posted.