There are 5 yellow pegs, 4 red pegs, 3 green pegs, 2 blue pegs, and 1 orange peg to be placed on a triangular peg board. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two pegs of the same color?

**Answer Choices**

A. 0

B. 1

C. 5 ! \cdot 4 ! \cdot 3 ! \cdot 2 ! \cdot 1 !

D. 15 ! /(5 ! \cdot 4 ! \cdot 3 ! \cdot 2 ! \cdot 1 !)

E. 15 !