Questions: Using the digits 0,1,2, ... 8,9, determine how many 8-digit lock combinations are possible according to the following criteria. Zero cannot be used for the first digit; digits may be repeated. The number of possible 8-digit lock combinations is .

Using the digits 0,1,2, ... 8,9, determine how many 8-digit lock combinations are possible according to the following criteria. Zero cannot be used for the first digit; digits may be repeated.

The number of possible 8-digit lock combinations is .

Transcript text: Using the digits $0,1,2, \ldots 8,9$, determine how many 8 -digit lock combinations are possible according to the following criteria. Zero cannot be used for the first digit; digits may be repeated. The number of possible 8-digit lock combinations is $\square$ .

Solution

Solution Steps

Step 1: Identify the constraints

The combination is 8 digits long.
The first digit cannot be 0.
Digits can be repeated.

Step 2: Determine the number of choices for each digit

For the first digit, there are 9 possible choices (1 through 9).
For the remaining 7 digits, each can be any of the 10 digits (0 through 9).

Step 3: Calculate the total number of combinations

The total number of combinations is the product of the number of choices for each digit.
This is calculated as \( 9 \times 10^7 \).

The number of possible 8-digit lock combinations is \( 9 \times 10^7 \).

Final Answer

\(\boxed{90000000}\)

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