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?

(A) P(B and V)=10%
(B) P(B and V)=20%
(C) P(B and V)=30%
(D) P(B and V)=40%

Answer 1

Answer: Option A

P(B and V)=10%

Step-by-step explanation:

To solve this poroblema we use the formula of combinations:

$nCr =\frac{n!}{r!(n-r)!}$

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:

$5C2$

$5C2=\frac{5!}{2!(5-2)!}$

$5C2=10$

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:

$P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%$

Answer 2

Answer: the answer is D

Step-by-step explanation:

Cause you have to do 100% divided by 5 you will get 20%

So if you have two of the five colors you will have two multiple 20% times 2 and get 40%