Problem Analysis:

You are tasked with selecting a 3-number code from a set of 27 numbers without allowing repetition, and the order of selection matters.

This is a permutation problem since the order of the numbers in the code matters.

Calculation:

To find the number of unique codes, calculate the permutation of choosing 3 numbers from 27 without repetition:

$P(27, 3) = 27 \times 26 \times 25$

Solution:

$27 \times 26 = 702$ $702 \times 25 = 17,550$

Thus, there are 17,550 unique codes possible.

Would you like additional details or clarifications?

Related Questions:

1. How does the problem change if repetition of numbers is allowed?
2. What if the code uses more or fewer digits (e.g., 4-digit or 2-digit codes)?
3. How can combinations differ