A password is made by arranging 2 distinct letters followed by 2 distinct digits (0-9). How many such passwords can be created?

Official Answer

Certainly! Let's dive into this interesting probability question. To begin with, the task at hand requires us to calculate the number of possible passwords made by arranging 2 distinct letters followed by 2 distinct digits, where all characters are distinct.

Given the English alphabet consists of 26 letters, and there are 10 digits (0-9), the method to approach this is by breaking down the problem into smaller, manageable parts and applying the fundamental principle of counting.

For the first part of the password, which consists of 2 distinct letters, we select the first letter from the 26 available options. Once the first letter is chosen, we're left with 25 options for the second letter, as it needs to be distinct from the first.

Therefore, the total number of ways to choose 2 distinct letters is 26 options for the first letter multiplied by 25 options for the second, giving us a subtotal of 26 * 25.

Moving on to the second part of the password, which consists of 2 distinct digits, we apply a similar logic. There are 10 options for the first digit. Once that is selected, we have 9 remaining options for the second digit to ensure it's distinct from the first.

Consequently, for the digits, we have 10 options for the first digit multiplied by 9 for the second, resulting in a subtotal of 10 * 9.

To find the total number of such passwords, we combine these two parts. Since the choice of letters and digits are independent events, we multiply the subtotal of the letters part by the subtotal of the digits part.

Thus, the total number of possible passwords is (26 * 25) * (10 * 9). Simplifying this, we get 26 * 25 * 10 * 9 = 65,000.

In conclusion, there are 65,000 unique passwords that can be created by arranging 2 distinct letters followed by 2 distinct digits. This solution not only demonstrates a clear understanding of the combinatory principles but also showcases an analytical approach to problem-solving. It's crucial in roles that demand a strong foundation in probability and statistics, such as a Data Scientist or Data Analyst position, to be able to deconstruct and solve complex problems systematically. By personalizing this framework based on your experiences and strengths, you can effectively communicate your analytical capabilities and problem-solving skills in your interviews.