You have a bike lock with a 4-digit combination. Each space can be any number 0 – 9. The only restriction is none of the numbers can be duplicated once they are used. How many possible combinations can be formed?

To solve the problem, we need to calculate the number of possible 4-digit combinations where each digit is unique (i.e., no digit is repeated).

1. **First digit:** There are 10 possible digits (0-9) available for the first digit.
2. **Second digit:** After choosing the first digit, 9 digits remain, so there are 9 possible choices for the second digit.
3. **Third digit:** After choosing the first two digits, 8 digits remain, so there are 8 possible choices for the third digit.
4. **Fourth digit:** After choosing the first three digits, 7 digits remain, so there are 7 possible choices for the fourth digit.

The total number of possible combinations can be found by multiplying these values:

\[
10 \times 9 \times 8 \times 7 = 5040
\]

So, there are **5,040 possible combinations** for the bike lock.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How would the number of combinations change if the digits could be repeated?
2. What if the lock had 5 digits instead of 4 with no repeated digits?
3. How would you calculate the probability of guessing the correct combination on the first try?
4. What if the combination had to start with an even digit?
5. How does this problem change if the lock were alphanumeric instead of just digits?

**Tip:** When dealing with permutations (arrangements without repetition), remember that the number of available choices decreases with each selection.

Explore how to calculate the total number of unique 4-digit combinations for a bike lock when each digit can only be used once. This problem involves combinatorial concepts like permutations and is suitable for students in Grades 8-10.

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