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?

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