Write the greatest 7-digit number having three different digits.

Since we have to write the greatest 7-digit number having 3 different digits, we will pick up the three greatest digits 7, 8, 9 out of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Therefore, the greatest 7-digit number is 9999987.