Question

For spirit day, each 8th-grade homeroom designs a unique two-color t-shirt. They get to choose from the colors red, blue, green, violet, and orange. Each t-shirt is a solid color with a different color used for the student's name. What is the probability that a homeroom will have a t-shirt with the combo of blue and violet?

Answer 1

The probability of a homeroom having a blue and violet t-shirt when choosing from five different colors is 1/10 or 10% since there is only one blue and violet combination out of a total of 10 possible two-color combinations.

Step-by-step explanation:

To answer the probability question, we must determine how many possible two-color combinations there are with the given color choices, and then identify how many of those combinations are of blue and violet. Given the colors red, blue, green, violet, and orange, there are a total of 5 colors to choose from. To design a shirt with two colors without repeating the same color, we use combinations. The formula for combinations is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

In this case, n is 5 (total colors) and k is 2 (colors for the shirt). Thus, the total number of two-color combinations we can make is C(5, 2) = 5! / (2!(5-2)!) = 10 combinations.

There is only one combination of blue and violet. Therefore, the probability of a homeroom having a t-shirt with blue and violet is 1/10 or 10%.