Question

In another state, all license plates consist of 6 symbols chosen from the 26 letters of the alphabet and the digits 0-9. How many license plates are possible if no repetitions are allowed and there must be exactly 3 letters followed by 3 numbers

Answer 1

Answer:

11,232,000 license plates are possible.

Step-by-step explanation:

The order in which the symbols are chosen is important(ABC is a different plate than BAC), which means that the permutations formula is used 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:

3 letters from a set of 26.

3 digits from a set of 10. So

$T = P_{26,3}P_{10,3} = \frac{26!}{23!} \times \frac{10!}{7!} = 11232000$

11,232,000 license plates are possible.