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.
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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).
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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)
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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.
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Total Combinations Calculation: Since each number can be chosen independently, you multiply the number of choices for each position: \[ \text{Total Combinations} = 50 \times 50 \times 50 = 50^3 \]
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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.