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

Answer 1

Answer:

There are 151,200 possible license plates.

Step-by-step explanation:

The order in which the digits are positioned is important(for example, 012345 is a different plate than 102345). No repeat digits are allowed, which means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this question:

There are 10 possible digits(from 0 to 9).

The plate has 6 slots.

So

$P_{(10,6)} = \frac{10!}{(10-6)!} = 151200$

There are 151,200 possible license plates.