111. How many five-digit natural numbers can be formed using the digits 1 and 0 if the digit 1 appears exactly three times in each number?
$\triangle$ We will search for the specified numbers by enumeration, ensuring that we do not miss any number. It is simpler to start by finding the positions for the two zeros, because if the positions for the zeros are determined, the three remaining positions will be filled with ones uniquely.

Let's fix one of the zeros in the second position; then the other zero can be placed in the third, fourth, or fifth positions. If we now fix one zero in the third position, the second zero can be placed in the fourth or fifth positions (the case where zeros are in the third and second positions has already been considered). Finally, if we fix one zero in the fourth position, the other zero can only be placed in the fifth position. This gives us the following 6 numbers:

$$
10011,10101,10110,11001,11010,11100 .
$$

## Answer: 6 .