## Suppose in a state, license plates have two letters followed by four numbers, in a way that no letter or number is repeated in a single plat

Question

Suppose in a state, license plates have two letters followed by four numbers, in a way that no letter or number is repeated in a single plate. Determine the number of possible license plates for this state

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2 weeks 2021-09-13T23:49:48+00:00 1 Answer 0

3,276,000 possible license plates for this state

Step-by-step explanation:

The order is important. For example, if the letters are EM, it is already a different plate than if the letters were ME. So 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: Letters

There are 26 letters in the alphabet. In the plate, there are two letters. So permutations of two from a set of 26. Digits

There are 10 digits. In the plate, there are four. So permutations of 4 from a set of 10 Total

Multiplying these values

650*5040 = 3,276,000

3,276,000 possible license plates for this state