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

11,232,000 license plates are possible.

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)) = (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) = (26!)/(23!) * (10!)/(7!) = 11232000`

11,232,000 license plates are possible.