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 pl

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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

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Diễm Kiều 1 day 2021-07-22T14:53:20+00:00 1 Answers 1 views 0

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    2021-07-22T14:55:07+00:00

    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.

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