Question

Using the digits 0, 1, 2, ...8, 9, determine how many 8-digit lock combinations are possible according to the following criteria?

Answer 1

To determine the number of 8-digit lock combinations using the digits 0-9 and following certain criteria, we start with 10 options for each digit and subtract restricted options. There are a total of 874,800 combinations.

Step-by-step explanation:

To determine the number of 8-digit lock combinations using the digits 0-9, we need to consider the following criteria:

1. The first digit cannot be 1 or 2, as it is rounded up to 2 and dropped.
2. The second digit is dropped.
3. The third digit cannot be 7 or 8, as it is rounded up to 8 and replaced by 0.
4. The fourth digit is replaced by 0.
5. The fifth digit is replaced by 0.

To calculate the number of combinations, we start with 10 options for each digit, but we need to subtract the restricted options. Therefore, the number of combinations is (10-2) * (10-1) * (10-2) * (10-1) * (10-1) * 10 * 10 * 10 = 2 x 9 x 2 x 9 x 9 x 10 x 10 x 10 = 874,800 combinations.