The number of ways in which the 4 faces of a regular tetrahedron can b...
Analysis:
A regular tetrahedron is a polyhedron with four triangular faces, all of which are equilateral triangles. Each face can be painted with one of the four given colors. To find the number of ways in which the faces can be painted, we can use the concept of permutations.
Solution:
To find the number of ways to paint the faces of a regular tetrahedron, we can consider the faces one by one.
Face 1:
There are 4 different colors available, so the first face can be painted in 4 different ways.
Face 2:
For each color chosen for the first face, there are now 3 remaining colors available. Hence, the second face can be painted in 3 different ways.
Face 3:
For each color combination chosen for the first two faces, there are now 2 remaining colors available. Hence, the third face can be painted in 2 different ways.
Face 4:
For each color combination chosen for the first three faces, there is only 1 remaining color available. Hence, the fourth face can be painted in 1 different way.
Total number of ways:
To find the total number of ways to paint the faces of the tetrahedron, we multiply the number of choices for each face together.
Total = 4 * 3 * 2 * 1 = 24
Therefore, the correct answer is option B, 24.