Tonya and Lauren are designing a soccer uniform. They want to use two colorson the shirt. Their choices are green,orange,yellow, purple, blue, and silver.How many ways can they choose two colors?

g, o

g, y
g, p
g, b
g, s

Continue with the other color combinations.

How many do you get?

I'm not positive, but I think you do it like this. Check my work based on your notes/textbook.

6C2=6!/(6-2!)2!=6!/4!2!=6X5X4X3X2/4X3X2X2=(cross out 4x3x2 on the top and bottom)=30/2=15

6 ways

To determine the number of ways Tonya and Lauren can choose two colors for the soccer uniform, we can use the concept of combinations. The number of ways to choose two colors from a set of six can be calculated using the formula for combinations, which is:

nCr = n! / ((n-r)! * r!)

Where n is the total number of colors available and r is the number of colors to be chosen.

In this case, n = 6 (since there are six color choices) and r = 2 (since they want to choose two colors). Plugging these values into the formula, we get:

6C2 = 6! / ((6-2)! * 2!)

Simplifying further:

6C2 = 6! / (4! * 2!)

Using the factorial notation, where n! represents the product of all positive integers less than or equal to n:

6! = 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
2! = 2 * 1

Substituting these values into the formula:

6C2 = (6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (2 * 1))

Canceling out common terms:

6C2 = (6 * 5) / (2 * 1)

Calculating:

6C2 = 30 / 2

6C2 = 15

Therefore, there are 15 different ways for Tonya and Lauren to choose two colors for their soccer uniform from the given choices of green, orange, yellow, purple, blue, and silver.