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

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    2021-09-13T23:51:38+00:00

    Answer:

    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:

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

    Letters

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

    P_{(26,2)} = \frac{26!}{24!} = 650

    Digits

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

    P_{(10,4)} = \frac{10!}{6!} = 5040

    Total

    Multiplying these values

    650*5040 = 3,276,000

    3,276,000 possible license plates for this state

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