Question

A government agency hires you to provide consulting on new rules regarding vehicle license plates. The agency is considering an all-numbers license plate that has six slots (digits 0-9 with no duplicate digits allowed). How many possible license plates are there?

Acceptable license plate: 134-058

Unacceptable license plate: 114-432 (duplicates)

Group of answer choices

1,000,000

248,480

60,480

151,200

Answer 1

The license plate has 6 plots, with digits from 0 to 9, with no duplicates allowed.

Now, from 0 to 9, there are 10 digits.

We have to find the number of possible license plates.

Now, the first digit of the license plate can have 10 digits, because there are 10 digits from 0 to 9. So, the first digit can be written in 10 number of ways.

Now, the second digit of the license plate can have 9 digits, as the first place digit cannot be used anymore. So, the second digit can be written in 9 number of ways.

For any of these choices, the third digit can have 8 digits, as the first two place digits cannot be used anymore. So, the third digit can be written in 8 number of ways.

Similarly, the fourth digit can be written in 7 ways; the fifth can be written in 6 ways; and the sixth, ie. the last, in 5 ways.

So, by multiplication rule of combination, the number plate can be written in

10*9*8*7*6*5 ways,

ie. 151200 ways.

So, the possible number of ways in which the number plate can be written is 151200.

So, the correct answer is (D) 151200.