The problem described asks for the number of ways to enter a five-digit code on a keypad with numbers 0-9, where each number may not be used more than once, and the order of the digits matters. This is a permutation problem because the order in which the numbers are entered is important.

To calculate the number of ways to select 5 digits out of the 10 available (0 through 9), we use the permutation formula:

$P(n, r) = \frac{n!}{(n - r)!}$

Where:

• $n = 10$ (since there are 10 digits: 0-9),
• $r = 5$ (since we need a 5-digit code).

The formula for this scenario is:

$P(10, 5) = \frac{10!}{(10 - 5)!} = \frac{10!}{5!}$

You should leave the answer as $P(10, 5)$ without evaluating the factorials, as requested.

Would you like more details on this problem or have any questions? Here are some related questions you might find helpful:

1. How do you differentiate between permutations and combinations?
2. Can you explain how to use factorial notation in permutation and combination problems?
3. What are some real-life applications of permutations and combinations?
4. How does the formula for permutations change if repetition is allowed?
5. How do you calculate permutations when there are repeated elements?

Tip: Always remember that if the order of selection matters, it's a permutation problem, and if the order doesn't matter, it's a combination problem.