Determine the number of ways the faces of a regular tetrahedron can be colored with three colors

Tetrahedron is a geometrical figure or solid that is formed in similar manner as a pyramid. The faces of the formed pyramid are triangles. Also is the base.

By the statement above, it can be deduced that the figure has four sides. The number of ways in which the sides can be colored by any of the three (3) colors is,

3 x 3 x 3 x 3 = 81

Since the sides can still have the same colors, we deduct this value by 3 in order to eliminate the uniform colors of the four sides.

= 81 - 3 = 78

Also, we can eliminate the concern on only two colors can mix,

= 3 x 2 = 6

Subtracting,

78 - 6 = 72

Hence, the answer is 72.