Question

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 .........

Answer 1

• 200,000 6-digit numbers can be constructed.

Step-by-step 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.