How many numbers are there between 1000 and 2000 such that even digit is either 0, or 1, or 2?a)54 b)27c)10S d)noneCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

To solve this problem, we need to find the number of integers between 1000 and 2000 such that the units digit is either 0, 1, or 2.

Since the units digit can only be 0, 1, or 2, we have three possible choices for the units digit. For the thousands, hundreds, and tens digits, we have 10 choices (0-9) for each digit.

To find the total number of integers between 1000 and 2000 that satisfy the given condition, we multiply the number of choices for each digit.

Here's the breakdown:

- Thousands digit: We have 10 choices (0-9) for the thousands digit.
- Hundreds digit: We have 10 choices (0-9) for the hundreds digit.
- Tens digit: We have 10 choices (0-9) for the tens digit.
- Units digit: We have 3 choices (0, 1, 2) for the units digit.

To find the total number of integers, we multiply these choices together:

10 choices × 10 choices × 10 choices × 3 choices = 3000

So, there are 3000 numbers between 1000 and 2000 such that the units digit is either 0, 1, or 2.

However, the question asks for the number of integers between 1000 and 2000 that satisfy the given condition. Since there are no integers between 1000 and 2000 that have a units digit of 2, the correct answer is option 'D' (none).

In summary, there are no numbers between 1000 and 2000 such that the even digit is either 0, 1, or 2.

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