Let a language $\Sigma$ have 16 letters, we have a message in that language that was encrypted using monoalphabetic substitution (a permutation of the alphabet) and we want to break it.
We also noticed the message uses only 10 letters from $\Sigma$. How many tries will it take on average to break using brute force? (or how many possible combinations there are?)
I think the total is ${16 \choose 10}10!$
${16 \choose 10}$ choose a subset of letters
$10!$ is a permutation of those letters
But don't we need to consider the length of the message as well? (it wasn't mentioned in the question)