Question

rafael will randomly select 3 shirts from his closet and pack all 3 shirts in his suitcase. there are only 8 shirts in his closet: 5 are blue, and 3 are red. what is the probability, to the nearest 0.01, that rafael will select 3 blue shirts?
0.01
o. 0.04
c 0.12
o 0.18
0.24

Explanation:

Step1: Calculate the number of ways to choose 3 shirts from 8

The combination formula is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 8\) and \(r=3\).

$$C(8,3)=\frac{8!}{3!(8 - 3)!}=\frac{8\times7\times6}{3\times2\times1}=56$$

Step2: Calculate the number of ways to choose 3 blue shirts from 5

Using the combination formula with \(n = 5\) and \(r = 3\)

$$C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5\times4}{2\times1}=10$$

Step3: Calculate the probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

$$P=\frac{C(5,3)}{C(8,3)}=\frac{10}{56}\approx0.18$$

Answer:

D. 0.18