Asked by Anonymous

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?

Answers

Answered by Stephanie
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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