I want to compute the number of numbers of length $N$ , such that
count of digit 5 is 2 and
count of digit 7 is 3. The rest of the places can be filled by any digits i.e. repetition is allowed.
Can I directly calculate it or do I have to make cases?
For example, below are some valid numbers of length $8$, where count of $5$ is $2$ and count of $7$ is $3$.