How many possible transponder codes consisting of four numbers from zero to seven are available?

To determine the total number of possible transponder codes consisting of four numbers, where each number can range from zero to seven, you need to consider the number of choices available for each position in the code.

Since each digit in the code can be any number from zero to seven, there are a total of 8 possible choices (0, 1, 2, 3, 4, 5, 6, 7) for each digit. The transponder code consists of four such digits.

To find the total number of combinations, you multiply the number of choices for each digit together:

8 choices for the first digit

× 8 choices for the second digit

× 8 choices for the third digit

× 8 choices for the fourth digit

This results in:

8 × 8 × 8 × 8 = 8^4

Calculating 8^4 gives:

8^4 = 4096

Thus, there are a total of 4096 different possible transponder codes that can be created using four numbers, each ranging from zero to seven. This robust method for calculating the combinations is a fundamental concept in combinatorics, which is valuable in a variety of fields, including aviation and