Zip code contains 4 digits. How many zip-codes can be created with digits 0−9 if you can use each digit only once and zip code can not start with 0.
4 digits be pull out from numbers (0-9)
Just so you know (0-9)=(0,1,2,3,4,,5,6,7,8,9)=10digit
Digit 1 no zero we have (1-9) possibilities 9
Digit 2 zero can be included we have(0,1,2,3,4,5,6,7,8,) possibilities 9
Digit 3?
Digit 4?
Now would be
The complete possibilities would be??
9×9××??
oops. I allowed repetition. my bad.
To determine the number of possible zip codes, we can break down the problem step by step:
1. Determine the number of choices for the first digit of the zip code:
Since the zip code cannot start with 0, we have 9 options (digits 1-9) for the first digit.
2. Determine the number of choices for the second digit:
After selecting the first digit, we have 9 remaining digits (0 and the remaining digits from 1-9) for the second position.
3. Determine the number of choices for the third digit:
After selecting the first two digits, we have 8 remaining digits for the third position.
4. Determine the number of choices for the fourth digit:
Finally, after selecting the first three digits, we have 7 remaining digits for the fourth position.
To find the total number of possible combinations, we multiply the number of choices for each position together:
9 options for the first digit * 9 options for the second digit * 8 options for the third digit * 7 options for the fourth digit.
Therefore, the total number of zip codes that can be created is:
9 * 9 * 8 * 7 = 4,536 zip codes.