In each of the following exercises use Corollary 17 .2 to work the problem, even though the answer might be obtained by more elementary methods.

Find the number of distinguishable tetrahedral dice that can be made using one, two, three, and four dots on the faces of a regular tetrahedron, rather than a cube.  

Data from 17.2 Corollary 

If G is a finite group and X is a finite G-set, then number of orbits in X under G) 

Proof:  The proof of this corollary follows immediately from the preceding theorem.

Transcribed Image Text:

1 |G| ΣΧ geG