AMC 10 2000 Problem 13

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 !

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