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How many 5 digit numbers have at least one zero digit?
- a)30951
- b)40141
- c)47132
- d)50001
- e)50433
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many 5 digit numbers have at least one zero digit?a)30951b)40141c)...
Understanding the Problem
To find how many 5-digit numbers have at least one zero digit, we can use the principle of complementary counting. This means we will first calculate the total number of 5-digit numbers, and then subtract the number of 5-digit numbers that do not contain the digit '0'.
Total Number of 5-Digit Numbers
- The range of 5-digit numbers is from 10000 to 99999.
- The total count is:
Counting 5-Digit Numbers Without Zero
- A 5-digit number cannot start with '0', so the first digit can be any of 1-9 (9 choices).
- The remaining four digits can be any of 1-9 (9 choices each).
Calculating Numbers With At Least One Zero
- Now, subtract the total number of 5-digit numbers without a zero from the total number of 5-digit numbers:
Conclusion
- Therefore, the total number of 5-digit numbers that contain at least one '0' digit is **30951**.
- The correct answer is option 'A'.
To find how many 5-digit numbers have at least one zero digit, we can use the principle of complementary counting. This means we will first calculate the total number of 5-digit numbers, and then subtract the number of 5-digit numbers that do not contain the digit '0'.
Total Number of 5-Digit Numbers
- The range of 5-digit numbers is from 10000 to 99999.
- The total count is:
- 99999 - 10000 + 1 = 90000
Counting 5-Digit Numbers Without Zero
- A 5-digit number cannot start with '0', so the first digit can be any of 1-9 (9 choices).
- The remaining four digits can be any of 1-9 (9 choices each).
- Choices for the first digit: 9
- Choices for each of the next four digits: 9
- Total without zero: 9 * 9 * 9 * 9 * 9 = 9^5 = 59049
Calculating Numbers With At Least One Zero
- Now, subtract the total number of 5-digit numbers without a zero from the total number of 5-digit numbers:
- Numbers with at least one zero = Total 5-digit numbers - Numbers without zero
- Numbers with at least one zero = 90000 - 59049 = 30951
Conclusion
- Therefore, the total number of 5-digit numbers that contain at least one '0' digit is **30951**.
- The correct answer is option 'A'.
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