jmc

The probability that two coins land tails and five coins land heads, in some order, is ${\left(\frac{3}{4}\right)}^2{\left(\frac{1}{4}\right)}^5=\frac{9}{16384}$. Any two of the seven coins can be tails, so this can happen in $\left(\genfrac{}{}{0ex}{}{7}{2}\right)=21$ ways. Therefore, the probability that exactly two coins come up tails is $21\cdot \frac{9}{16384}=\boxed{\frac{189}{16384}}$.