How many combinations does a 3-digit lock have?
Understand the Problem
The question is asking for the number of possible combinations for a 3-digit lock. Typically, a combination lock allows digits from 0 to 9, which means each digit has 10 possible values. We will calculate the total combinations by considering all possible values for each of the three digits.
Answer
The total number of possible combinations for the 3-digit lock is $1000$.
Answer for screen readers
The total number of possible combinations for the 3-digit lock is $1000$.
Steps to Solve
- Identify the number of choices for each digit
Since the lock has 3 digits and each digit can be any number from 0 to 9, there are a total of 10 choices for each digit.
- Calculate the total combinations
To find the total number of combinations for the lock, multiply the number of choices for each digit together:
$$ \text{Total Combinations} = \text{Choices for Digit 1} \times \text{Choices for Digit 2} \times \text{Choices for Digit 3} $$
This gives:
$$ \text{Total Combinations} = 10 \times 10 \times 10 $$
- Perform the final multiplication
Now we calculate the multiplication:
$$ 10 \times 10 \times 10 = 1000 $$
Thus, the total number of combinations for the lock is 1000.
The total number of possible combinations for the 3-digit lock is $1000$.
More Information
A 3-digit combination lock, where each digit can range from 0 to 9, offers a surprisingly large number of combinations. This principle can be applied to any scenario involving multiple independent choices, showcasing the power of combinatorial counting.
Tips
- Forgetting that the same digit can be used more than once, which is allowed in this case, leading to an undercount of combinations.
- Confusing the calculation with cases where the digits must be unique, which is not applicable here.