Probability
# Rule of Sum and Rule of Product

How many ways are there to elect one president and one vice president from $25$ candidates?

**Details and assumptions**

The president and vice president cannot be the same person.

How many ways are there to color the above regions with 3 different colors, if adjacent regions should have different colors?

**Note:** You need not use all three colors of paint but each region must be colored by any one of them.