Question

A security company requires its employees to have a 7-character computer password that must consist of 5 letters and 2 digits. How many passwords can be made if no digit or letter may be replaced?

Answer 1

There are 7,893,600 unique 7-character passwords possible, derived from the combination of choosing 5 distinct letters and 2 distinct digits without replacement.

Step-by-step explanation:

The student is asking how many unique 7-character passwords can be created given a specific set of rules. To solve this, we consider the combination of 5 letters and 2 digits. With 26 possibilities for each letter and 10 possibilities for each digit, provided that no character is repeated, the calculation would be as follows:

1. Choose 5 distinct letters from 26, without replacement: 26 × 25 × 24 × 23 × 22
2. Choose 2 distinct digits from 10, without replacement: 10 × 9
3. Multiply these two results to get the total number of possible passwords: (26 × 25 × 24 × 23 × 22) × (10 × 9)

When calculated, the total number of possible passwords equals 7,893,600.