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Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

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How many 3-digit even numbers are there, which comprise of the digits 1, 2 and 3 in some order?

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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.

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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.

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