Home > A2C > Chapter 10 > Lesson 10.2.4 > Problem10-107

10-107.
1. On Friday, Randy Random went to DJ's to get a cone. Homework Help ✎

1. If he made a random selection, what is the probability that he got all three scoops the same?

2. What is the probability that he got all three different?

Once the first scoop is chosen, there is no choice for the second or third scoop.

$\frac{5}{1^{\text{st}}}\cdot \frac{1}{2^{\text{nd}}}\cdot \frac{1}{3^{\text{rd}}}=5\text{ ways}$

$P\text{(all the same)}=\frac{\text{number of ways all the same}}{\text{total number of ways}}=\frac{5}{5\cdot5\cdot5}$

$\frac{5}{125}=0.04$

Since the order does matter, it is the number of ways 3 out of 5 scoops can be arranged.

$\frac{5\cdot4\cdot3}{125}$