For Spirit Day, each 8th-grade homeroom designs a unique twocolor T-shirt. They get to choose from the colors red (R), blue (B), green (G), violet (V), and orange (O). 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 a combination of blue and violet?

P(B and V)=10%

Step-by-step explanation:To solve this poroblema we use the formula of combinations:

C(n,r)=(nr)=n!(r!(n−r)!)

Where n is the number of objects that can be chosen and you choose r from them.

There are 5 colors of shirts.

The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:

5C2=

5C2=10

The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:

2C2=1

Then the probability is:

P( B and V)=

=0.1= 10%