Question
The lock is numbered from 0 to 49. Each combination uses three numbers in a right, left, right pattern. Find the total number of possible combinations for the lock. EVERY possible combination
Answers
GPT-4o mini
To find the total number of possible combinations for a lock that is numbered from 0 to 49 using a right, left, right pattern with three numbers, we can analyze the problem step by step.
1. **Range of Numbers**: The lock has numbers ranging from 0 to 49, which gives us a total of 50 possible numbers (since it includes both endpoints).
2. **Combination Pattern**: The combination involves picking three numbers in a specific order:
- The first number (for the "right" turn)
- The second number (for the "left" turn)
- The third number (for the "right" turn again)
3. **Number of Choices**:
- For the first (right) number, you can choose any of the 50 numbers.
- For the second (left) number, you can again choose any of the 50 numbers.
- For the third (right) number, you can again choose any of the 50 numbers.
4. **Total Combinations Calculation**:
Since each number can be chosen independently, you multiply the number of choices for each position:
\[
\text{Total Combinations} = 50 \times 50 \times 50 = 50^3
\]
5. **Calculating \(50^3\)**:
\[
50^3 = 50 \times 50 \times 50 = 2500 \times 50 = 125000
\]
Thus, the total number of possible combinations for the lock is **125,000**.
1. **Range of Numbers**: The lock has numbers ranging from 0 to 49, which gives us a total of 50 possible numbers (since it includes both endpoints).
2. **Combination Pattern**: The combination involves picking three numbers in a specific order:
- The first number (for the "right" turn)
- The second number (for the "left" turn)
- The third number (for the "right" turn again)
3. **Number of Choices**:
- For the first (right) number, you can choose any of the 50 numbers.
- For the second (left) number, you can again choose any of the 50 numbers.
- For the third (right) number, you can again choose any of the 50 numbers.
4. **Total Combinations Calculation**:
Since each number can be chosen independently, you multiply the number of choices for each position:
\[
\text{Total Combinations} = 50 \times 50 \times 50 = 50^3
\]
5. **Calculating \(50^3\)**:
\[
50^3 = 50 \times 50 \times 50 = 2500 \times 50 = 125000
\]
Thus, the total number of possible combinations for the lock is **125,000**.