A large van is being used for a picnic. There will be 8 people riding in the van, and there are 8 seats in the van (one of which is the driv

Question

A large van is being used for a picnic. There will be 8 people riding in the van, and there are 8 seats in the van (one of which is the driver’s seat). One of the 8 people will have to drive, but only 4 of the people are licensed to drive the van. In how many different ways could the people seat themselves in the van so that they have a licensed driver

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Nho 3 years 2021-07-23T17:25:19+00:00 1 Answers 16 views 0

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  1. minhkhang
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    2021-07-23T17:27:08+00:00
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    Answer:

    The people can seat themselves in 20160 different ways.

    Step-by-step explanation:

    Arrangements of n elements:

    The number of arrangements of n elements is given by the following formula:

    A_{n} = n!

    In this question:

    For the first seat, that is, the driver seat, 4 possible people can sit.

    For the remaining 7 seats, the number of ways in which the people can sit is an arrangement of 7 elements. So

    T = 4*7! = 4*5040 = 20160

    The people can seat themselves in 20160 different ways.

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