On Friday, Randy Random went to DJ's to get a cone.

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

   Hint (a):

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

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

   More Help (a):

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

   Answer (a):

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

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

   Hint (b):

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

   More Help (b):

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