Out of 10 students, 2 will be chosen to ride in a car instead of a van on an upcoming field trip. Which statement best describes this situat

Question

Out of 10 students, 2 will be chosen to ride in a car instead of a van on an upcoming field trip. Which statement best describes this situation?

A. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

B. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

C. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.

D. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.

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Arya 1 month 2021-09-14T17:59:04+00:00 1 Answer 0

Answers ( )

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    2021-09-14T18:00:53+00:00

    Answer:

    D

    Step-by-step explanation:

    Firstly, since it is a selection question, we shall be using a combination approach.

    So here we are trying to select the best answer that describes that 2 out of 10 students are selected.

    Let’s consider the scenario below;

    selecting r out of n can be resolved using the combination nCr

    = n!/(n-r)!r!

    Now in this case, our n = 10 and r = 2.

    Thus, 10C2, we have ;

    10!/(10-2)!2! = 10!/8!2! = (10 * 9 * 8!)/8!2! = (10 *9)/2! = 90/2 = 45

    Thus, 10C2 = 45

    Here, the order of selection does not matter as we can select in random fashion. This makes option D correct

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45:7+7-4:2-5:5*4+35:2 =? ( )