Answer: [tex] 2^{n} -1[/tex]
Justification:
As told in the statement, n stands for the number of bits, and [tex] 2^{n} [/tex] is the highest number of ways n bits can be arranged in the system.
Now, Antonio wants to show that the character can collect one less key than that. So, that number is [tex] 2^{n} [/tex] less 1, which is what the formula [tex] 2^{n} [/tex] - 1 states.