Final answer:
To find the number of five-digit numbers with no consecutive digits the same, we multiply the number of choices for each digit, resulting in 59,049 unique numbers.
Step-by-step explanation:
The question asks us to calculate the number of five-digit numbers where no two consecutive digits are the same. To solve this, we employ combinatorial reasoning. The first digit can be any number from 1 to 9, giving us 9 options (0 cannot be the first digit as we need a five-digit number). For the second digit, we have 9 options as well (it can be any digit except the one chosen as the first). This same reasoning applies to each subsequent digit. Therefore, the total number of such numbers is the product of the options for each position: 9 × 9 × 9 × 9 × 9 = 59,049.