Math Problem Statement
A bike lock has a 4 digit combination. Each character can be any digit between 0-5. How many combinations are possible?
Solution
To find the number of possible combinations for the bike lock, we can use the principle of multiplication.
The lock has 4 digits, and each digit can be any of the digits from 0 to 5, which means there are 6 possible choices for each digit.
So, the total number of possible combinations is calculated as:
Now, let's compute this:
Thus, there are 1,296 possible combinations for the bike lock.
Would you like more details or have any questions? Here are some related topics:
- How would the number of combinations change if the lock had 5 digits?
- What if the digits could be any number from 0 to 9 instead?
- How many combinations would there be if repetition of digits wasn't allowed?
- Can we use this method for combinations in real-life scenarios like pin codes?
- What is the probability of guessing the correct combination on the first try?
- How does the combination count change with different base numbers?
- Can you explain the difference between permutations and combinations?
- What is the general formula for finding the number of combinations with n digits and k possible values per digit?
Tip: Remember, when solving combinatorial problems, determining whether the order matters is crucial!
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Multiplication Principle
Formulas
\( n^k \) for counting combinations
Theorems
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Suitable Grade Level
Grades 7-9