Calvin is playing a game of Dungeons and Dragons. In order to make it across the river, he needs to throw six standard 4-sided dice, and have their sum be a multiple of 5. How many different dice throws result in Calvin making it across the river?

**Details and assumptions**

The dice are considered distinct from each other.

A 4-sided dice is a (tetrahedron) dice which yields values of 1, 2, 3, 4.

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