Question

for spirit day, each 8th - grade homeroom designs a unique two - color 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%
p(b and v)=20%
p(b and v)=30%
p(b and v)=40%

Explanation:

Step1: Calculate total combinations

The number of ways to choose 2 - color combinations from 5 colors is $C_{5}^2=\frac{5!}{2!(5 - 2)!}=\frac{5\times4}{2\times1}=10$.

Step2: Determine favorable combinations

There is 1 favorable combination (blue - violet).

Step3: Calculate probability

$P=\frac{1}{10}=0.1 = 10\%$.

Answer:

$P(B\text{ and }V)=10\%$