Question

multiple choice
rikku has 2 black t - shirts, 1 white t - shirt, and 3 red t - shirts. he has 3 pairs of jeans and 3 pairs of shorts. he also has 5 different pairs of shoes.
rikku selects a top, bottom, and pair of shoes at random.
what are the odds rikku selects an outfit with a red or black shirt and a pair of jeans?
press to hear a reminder or hint for this problem.
be sure to combine the red and black shirts when finding the number of desirable outcomes.

Explanation:

Step1: Calculate total number of T - shirts

Total T - shirts = \(2 + 1+3=6\)
Number of red or black T - shirts = \(2 + 3=5\)

Step2: Calculate total number of bottoms

Total bottoms = \(3+3 = 6\)
Number of jeans = \(3\)
Shoes = \(5\) (constant for all cases)

Step3: Calculate number of desirable outfits

Using the counting principle \(N_{d}=5\times3\times5 = 75\)

Step4: Calculate total number of outfits

Using the counting principle \(N_{t}=6\times6\times5=180\)

Step5: Calculate number of non - desirable outfits

\(N_{nd}=180 - 75=105\)

Step6: Calculate the odds

Odds = \(\frac{N_{d}}{N_{nd}}=\frac{75}{105}=\frac{5}{7}\)

Answer:

The odds are \(5:7\)