Hello, billym!

I'll assume that 500 and 5000 are included.

Three-digit numbers: _ _ _(1) Find the number of integers between 500 and 5000 that do not contain 0 as a digit.

They can begin with: {5, 6, 7, 8, 9} . . . 5 choices.

. . There are 9 choices for the second digit.

. . There are 9 choices for the third digit.

There are: . three-digit numbers with no 0s.

Four-digit numbers: _ _ _ _

They can begin with: {1, 2, 3, 4} . . . 4 choices.

. . There are 9 choices for each of the other 3 digtits.

There are: . four-digit numbers with no 0s.

Therefore, there are: . numbers with no 0s.

Three-digit numbers: _ _ _(2) How many integers between 500 and 5000 contain the digit 0 exactly once?

They can begin with: {5, 6, 7, 8, 9} . . . 5 choices.

. . There are 2 choices for the position of the 0.

. . There arte 9 choices for the third digit.

There are: three-digit numbers with one 0.

Four-digit number: _ _ _ _

They can begin with: {1, 2, 3, 4} . . . 4 choices.

. . There are 3 choices for the position of the 0.

. . There are: choices for the other two digits.

There are: four-digit numbers with one 0.

Therefore, there are: . numbers with exactly one 0.

From 500 to 5000, there are: . numbers.(3) ...at least twice?

3321 of them have no 0s.

1062 of them have one 0.

Therefore: . numbers with two or more 0s.