# Key, plaintext block and ciphertext block permutations question

Question: If a cipher’s key size is $$k$$ bits and its block size is $$b$$ bits, how many possible keys are there, how many possible plaintext blocks are there, and how many possible ciphertext blocks are there?

Studying for an exam and this popped up in a past paper without an answer, is the solution e.g. for key size $$2^k$$ bits? and similarly for the others will be $$2^b$$ bits? My friend thinks its $$b^k$$ so were unsure and clearly don't understand the logic behind it.

$$k$$-bit means the binary representation contains $$k$$ binary digits.
xx......xx : k binary digits

For each position can be 0 and 1 so, a $$k$$-bit can take $$2^k$$ distinct values.
You can similarly argue for $$b$$-bit block size, if you know that block size is the input size for block ciphers.