Answer :
Final answer:
The number of natural numbers less than 7000 that can be formed using the digits 0, 1, 3, 7, and 9 is 6250. The correct option is (a).
Explanation:
To find out the number of natural numbers less than 7000 that can be formed using the digits 0, 1, 3, 7, and 9 (with repetition allowed), we need to consider the digits in each place value.
- For the thousands place, any of the digits 0, 1, 3, 7, and 9 can be used. So, we have 5 choices.
- For the hundreds place, again, any of the digits 0, 1, 3, 7, and 9 can be used. So, we have 5 choices.
- For the tens place, we have 5 choices.
- For the units place, we have 5 choices.
As repetition of digits is allowed, we can multiply the number of choices available for each place value.
Therefore, the total number of natural numbers less than 7000 that can be formed using the given digits is:
5 (choices for thousands place) ×
5 (choices for hundreds place) ×
5 (choices for tens place) ×
5 (choices for units place) = 54 = 6250.
