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Five different colored flags will be placed on a pole , one beneath another . The arrangement of the colors indicates the message. How many messages are possible if five flags are to be selected from nine different colored flags?

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1 answer

  1. order matters so:

    Evalute the permutation 9P5
    A permutation is a way to order or arrange a set or number of things
    The formula for a combination of choosing r ways from n possibilities is:
    nPr = n!/
    (n - r)!

    where n is the number of items and r is the number of arrangements.
    Plugging in our numbers of n = 9 and r = 5 into the permutation formula:
    9P5 = 9!
    (9 - 5)!

    Remember that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

    Calculate the numerator n!:
    n! = 9!
    9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
    9! = 362,880

    Calculate the denominator (n - r)!:
    (n - r)! = (9 - 5)!
    (9 - 5)! = 4!
    4! = 4 x 3 x 2 x 1
    4! = 24

    Calculate our permutation value nPr for n = 9 and r = 5:
    9P5 = 362,880/ 24


    9P5 = 15,120 answer

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