Math Problem Statement

Each user in a computer system has a password which is 6 to 8 characters long where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there?

Solution

To

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Permutations and Combinations
Complementary Counting

Formulas

Total possible combinations = (choices for one character)^length
Using complementary counting to subtract invalid cases

Theorems

Complementary Counting Principle

Suitable Grade Level

Grades 10-12