Školjka

%V0 Let $f(k)$ be the number of all non-negative integers $n$ satisfying the following conditions: (1) The integer $n$ has exactly $k$ digits in the decimal representation (where the first digit is not necessarily non-zero!), i. e. we have $0 \leq n <10^k$. (2) These $k$ digits of n can be permuted in such a way that the resulting number is divisible by 11. Show that for any positive integer number $m,$ we have $f\left(2m\right) = 10 f\left(2m - 1\right)$.