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A lock has a code of 5 numbers from 1 to 10 . If no numbers in the code are allowed to repeat, how many different codes could be made? Answer:

A lock has a code of 55 numbers from 11 to 1010 . If no numbers in the code are allowed to repeat, how many different codes could be made?\newlineAnswer:

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Full solution

Q. A lock has a code of 55 numbers from 11 to 1010 . If no numbers in the code are allowed to repeat, how many different codes could be made?\newlineAnswer:
  1. Determine first digit choices: Determine the number of choices for the first digit of the code.\newlineSince there are 1010 numbers to choose from and no restrictions for the first digit, there are 1010 possible choices for the first number in the code.
  2. Determine second digit choices: Determine the number of choices for the second digit of the code.\newlineAfter choosing the first digit, there are 99 remaining numbers to choose from for the second digit, since no number can be repeated.
  3. Determine third digit choices: Determine the number of choices for the third digit of the code.\newlineSimilarly, after choosing the first two digits, there are 88 remaining numbers to choose from for the third digit.
  4. Determine fourth digit choices: Determine the number of choices for the fourth digit of the code.\newlineAfter the first three digits have been chosen, there are 77 remaining numbers to choose from for the fourth digit.
  5. Determine fifth digit choices: Determine the number of choices for the fifth and final digit of the code.\newlineAfter choosing the first four digits, there are 66 remaining numbers to choose from for the fifth digit.
  6. Calculate total number of codes: Calculate the total number of different codes that can be made.\newlineTo find the total number of different codes, multiply the number of choices for each digit together.\newlineTotal number of codes = 10×9×8×7×610 \times 9 \times 8 \times 7 \times 6
  7. Perform final multiplication: Perform the multiplication to find the final answer.\newlineTotal number of codes = 10×9×8×7×6=3024010 \times 9 \times 8 \times 7 \times 6 = 30240

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