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. 

Wooden cubes of the same size are to be painted a different color on each face to make children's blocks. How many distinguishable blocks can be made if eight colors of paint are available?

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