You can store the value as a number if you have a datatype that can represent more than choicescount possible values. In the case of 340, this is the number 12,157,665,459,056,928,801 which is just under 64 bits. So, you could hypothetically store this in a Unit64 (docs).
This isn't a good idea.
As soon as you add another question, you will overflow this datatype. That will make life very difficult for refactoring.
You've got something that isn't quite binary. This makes a mess of trying to decode it with binary operators. You can do it, but its veryvery uglyugly.
If anything changes (you remove a question) it becomes very fragile. It is easy to break this.
These things combined should firmly point you in the direction of a list of three value enums which can then be serialized. Don't worry about a specific number. Make it a nice structure that you can work from and then convert that into however you want to transmit it. When storing it in a database or the like, store it as a nice structure (not a big number).
Trying to pack things into bits doesn't make sense anymore. Memory is cheap. Its easier to transmit a 40 character long string that contains [ynm] that you an work with - clean code that you can reason about without getting a headache.