A library has 1,700,000 books, and the librarian wants to encode each using a codeword consisting of 3 letters followed by 3 numbers. Are there enough codewords to encode all 1,700,000 books with different codewords?
Please note that my solution differs from the authors’ one given at the end
Yes. There are 1,700,000 books and \(26^3 \cdot 10^3 = 17576000\) possible encodings which is more than the number of books
Authors’ answer: \(yes: 26^3 \cdot 10^3 > 5,000\)1
The authors’ calculation is the same but I don’t know where 5,000 comes from, possibly a typo?↩