A computer password consists of four characters: the first is one of the 10 digits 0–9, and each of the next three is one of the 26 uppercase letters of the English alphabet. Letters **may be repeated**. How many different passwords are possible?

Apply the multiplication principle. The choices are made sequentially and, because **repetition is allowed**, each letter slot is independent of the others. - 1st character: $10$ digits. - 2nd, 3rd, 4th characters: $26$ letters each. Total $= 10 \times 26 \times 26 \times 26 = 10 \cdot 26^{3} = 175{,}760$. - **B** ($156{,}000$) is the answer if repetition were **not** allowed — $10 \cdot 26 \cdot 25 \cdot 24$. The question explicitly allows repetition. - **A** counts only two choices, missing the last two letter slots. - **D** treats every slot as a digit *and* a letter — double-counting.