Exercise 229Combinatorics › Counting principlesHigh schoolAdded 3 Nov 2026

The product rule

#product rule#multiplication principle#independent choices

Statement

A password consists of $3$ letters (from the $26$ lowercase letters) followed by $4$ digits (from $0$ to $9$ ), with repetition allowed. How many passwords are possible?

Hint

Each choice is independent, so multiply.

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Solution

Choices. $26$ choices for each of $3$ letters, $10$ for each of $4$ digits.

Product rule. Total: $26^3\cdot10^4=17576\cdot10000=175{,}760{,}000$ .

Conclusion. There are $175{,}760{,}000$ possible passwords.

The product rule

Statement

Solution

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