Using the digits 0, 1, 2, ... 8, 9, determine how many 6 -digit numbers can be constructed according to the following criteria.

The number must be odd and greater than 600,000 ; digits may be repeated.

The number of 6 -digit numbers that can be constructed is ...

200,000 6-digit numbers can be constructed.

Explanation:

Since the number is greater than 600,000, the first digit must be 6, 7, 8, or 9, so 4 different options: 4

The second, third, fourth, and fith digits can be either number 0 through 9, so 10 options for each one: 10 * 10 * 10 * 10.

Since the number must be odd and greater than 600,00, the last digit is odd, so it can be 1, 3, 5, 7, or 9, so 5 different options: 5.

Using the multiplication counting principle, you muliply the independent options to obtain the number of different combinations:

4 * 10 * 10 * 10 * 10 * 5 = 200,000.