## Binomial coefficients divisible by 10

### Problem 322

Published on Sunday, 30th January 2011, 04:00 am; Solved by 305; Difficulty rating: 70%
Let T(`m`, `n`) be the number of the binomial coefficients ^{i}C_{n} that are divisible by 10 for `n` ≤ `i` < `m`(`i`, `m` and `n` are positive integers).

You are given that T(10^{9}, 10^{7}-10) = 989697000.

Find T(10^{18}, 10^{12}-10).