Math Problems

1. Color the six faces of a cube with six different colors, if seven colors are available and no color is to be used more than once. Find how many different such cubes can be made.

2. Three black, two red and one white beads are strung together to form a necklace, which can be rotated and turned over. Assuming that beads of the same color are indistinguishable, how many different kinds of necklaces can be made?

3. Find the number of essentially different ways to color to vertices of a square if six colors are available and no color is to be used more than once.