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Math  /  Discrete

Questionstudent arrange the schedule?
6. The state of Virginia's license plate has three letters followed by four digits. Assuming that any letter or digit can be used, how many different license plates are possible?

Studdy Solution

STEP 1

1. There are 26 letters in the English alphabet.
2. There are 10 possible digits (0 through 9).
3. Each letter and digit can be used multiple times.

STEP 2

1. Calculate the number of possible combinations for the letters.
2. Calculate the number of possible combinations for the digits.
3. Multiply the combinations of letters and digits to find the total number of possible license plates.

STEP 3

Calculate the number of possible combinations for the letters. Since there are 26 letters and each of the three positions can be any letter, we have:
26×26×26 26 \times 26 \times 26

STEP 4

Calculate the number of possible combinations for the digits. Since there are 10 digits and each of the four positions can be any digit, we have:
10×10×10×10 10 \times 10 \times 10 \times 10

STEP 5

Multiply the combinations of letters and digits to find the total number of possible license plates. We multiply the results from STEP_1 and STEP_2:
(26×26×26)×(10×10×10×10) (26 \times 26 \times 26) \times (10 \times 10 \times 10 \times 10)
=263×104 = 26^3 \times 10^4
=17,576×10,000 = 17,576 \times 10,000
=175,760,000 = 175,760,000
The total number of different license plates possible is:
175,760,000 \boxed{175,760,000}

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