Question 84
Compute the number of ways to pick a 3-element subset of
$$
\left\{10^{1}+1,10^{2}+1,10^{3}+1,10^{4}+1,10^{5}+1,10^{6}+1,10^{7}+1\right\}
$$
such that the product of the 3 numbers in the subset has no digits besides 0 and 1 when written in base 10.
$$
\left\{10^{1}+1,10^{2}+1,10^{3}+1,10^{4}+1,10^{5}+1,10^{6}+1,10^{7}+1\right\}
$$
such that the product of the 3 numbers in the subset has no digits besides 0 and 1 when written in base 10.