How many natural 4-digit numbers exist in which all of the digits are even?

256

Step-by-step explanation:

the first digit cannot be 0, so there are only 4 even numbers

For the second, third, and fourth digits, there are 5 available numbers.

Thus, the number of 4-digit numbers containing only even digits is 4 x 5 x 5 x 5 = 500

2nd place ( hundred place) can also be filled up by 4 number : 2, 4, 6, 8 and same logic applies to 3rd ( 10th ) and 4th( unit) .

so number of ways is 4*4*4*4= 256 ways .