Suppose a designer has a palette of 13 colors to work with, and wants to design a flag with 2 vertical stripes, all of different colors.
How many possible flags can be created?
choices for 1st vertical stripe = 13
choices for 2nd vertical stripe = 12
number of possible setups = (13)(12) = 156
all 2 of them?
13 * 12 = ____
Well, let me think... if the designer has 13 colors to work with and wants to create a flag with 2 vertical stripes, each of a different color, we can use a little math to figure out the possibilities.
For the first stripe, the designer can choose any of the 13 colors. Then, for the second stripe, they can choose any of the remaining 12 colors. So, the number of possible flags can be calculated by multiplying the number of options for each stripe together.
13 colors for the first stripe multiplied by 12 colors for the second stripe gives us a grand total of 156 possible flags. That's a lot of flag fun!
Of course, this assumes that the order of the stripes matters, and that we can count the same colors in a different order as distinct flags. Otherwise, we would need to divide by 2 to account for the duplicate color combinations.
But hey, let's keep it simple and go with 156 for now. Let your colorful creativity shine!
To find the number of possible flags that can be created, we need to calculate the number of ways we can choose 2 colors from a palette of 13 colors.
This can be calculated using the combination formula, which is given by:
C(n, k) = n! / (k! * (n-k)!)
where n is the total number of colors in the palette and k is the number of colors chosen for the stripes.
In this case, n = 13 (total number of colors in the palette) and k = 2 (number of colors chosen for the stripes).
Using the combination formula, we can calculate the number of possible flags:
C(13, 2) = 13! / (2! * (13-2)!)
= 13! / (2! * 11!)
= (13 * 12) / (2 * 1)
= 78
Therefore, there are 78 possible flags that can be created with a palette of 13 colors and 2 vertical stripes, each of different colors.
To determine the number of possible flags that can be created with 2 vertical stripes, each of different colors, we can use the concept of combination.
Combination is a mathematical concept that determines the number of ways to choose a specific number of items from a larger set, without considering their order. In this case, we want to select 2 colors from a palette of 13 colors.
To calculate the number of combinations, we can use the formula for combinations:
C(n, r) = n! / (r!(n - r)!)
Where n represents the total number of colors in the palette, and r represents the number of colors to be selected.
In this scenario, we have 13 colors to choose from (n = 13), and we want to select 2 colors (r = 2). Plugging the values into the formula:
C(13, 2) = 13! / (2! * (13 - 2)!)
Calculating further:
C(13, 2) = 13! / (2! * 11!)
Now, we need to compute the factorials:
13! = 13 * 12 * 11!
2! = 2 * 1
Substituting the values into the formula:
C(13, 2) = (13 * 12 * 11!) / (2 * 1 * 11!)
The factorial of 11! cancels out:
C(13, 2) = (13 * 12) / 2
Simplifying further:
C(13, 2) = 13 * 6
Therefore, there are 78 possible flags that can be created with 2 vertical stripes, all of different colors, using a palette of 13 colors.