SOLUTION: Suppose a designer has a palette of 11 colors to work with, and wants to design a flag with 4 vertical stripes, all of different colors. How many possible flags can be created?

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Question 1206563: Suppose a designer has a palette of 11 colors to work with, and wants to design a flag with 4 vertical stripes, all of different colors.
How many possible flags can be created?
Found 3 solutions by MathLover1, Theo, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
There are:
options for the first stripe
options for the second stripe
options for the third stripe
options for the fourth stripe
Therefore, the total number of possible flags is

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if he cares how the stripes are arranged, then the formula is p(11,4).

if he only cares about the colors and is not concerned with their position in the flag, then the formula is c(11,4).

since many flags have the same colors in different arrangement, then i would thin that p(11,4) would be more applicable.

c(11,4) = 11! / (4! * 7!) = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330

p(11,4) = 11! / (7!) = (11 * 10 * 9 * 8) = 7920

the difference between c(n,x) and p(n,x) is as follows.

suppose n = 3 and x = 2 and the 3 elements to choose from are ABC.

c(3,2) = 3! / 2! = (3 * 2 * 1) / (2 * 1) = 3.
p(3,2) = 3! / 1! = (3 * 2) = 6

the number of combinations is 3.
they are: AB, AC, BC
the number of permutations is 6.
they are: AB, BA, AC, CA, BC, CB.

with combinations, AB and BA are considered part of the same set because the order of the elements within the set is not important.

with permutations, AB and BA are considered different sets because the order of the elements within the set is important.

if two countries had the same colors and the same shape, then the only thing that would distinguish them would be the order of the colors in the flag.

i would go with the permutations number of 7920.

the possible ordering of the 4 different colors would be 4! = 4 * 3 * 2 * 1 = 24.

if you take that away, then you get the number of combinations because 7920 / 24 = 330.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Suppose a designer has a palette of 11 colors to work with, and wants to design
a flag with 4 vertical stripes, all of different colors.
How many possible flags can be created?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

First  vertical strip can be any of 11 colors.

Second vertical strip can be any of remaining 10 colors.

Third  vertical strip can be any of remaining  9 colors.

Fourth vertical strip can be any of remaining  8 colors.


Hence, the total number of differently colored flags is the product
of four integer numbers, starting from 11, in descending order

    11*10*9*8 = 7920.    <<<---===  ANSWER

Solved.



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