How many four-digit natural numbers are there such that all of the digits are even?

Correct option is B

Concept:
1. The first digit (thousands place) cannot be 0 (since it must be a four-digit number).
2. The other digits (hundreds, tens, and units places) can be any of the even digits, including 0.
1. Thousands place: The thousands place can be filled by any of the even digits except 0. Therefore, there are 4 choices (2, 4, 6, 8).
2. Hundreds place: The hundreds place can be any of the 5 even digits (0, 2, 4, 6, 8). Therefore, there are 5 choices.
3. Tens place: The tens place can be any of the 5 even digits (0, 2, 4, 6, 8). Therefore, there are 5 choices.
4. Units place: The units place can be any of the 5 even digits (0, 2, 4, 6, 8). Therefore, there are 5 choices.
Solution:
Let,
0, 2, 4, 6, 8

Thus, the number of four-digit natural numbers where all digits are even is 500.