MathDB
Peg positions

Source:

March 3, 2006
countingdistinguishabilityratioAMC 10

Problem Statement

There are 55 yellow pegs, 44 red pegs, 33 green pegs, 22 blue pegs, and 11 orange peg 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?
[asy] unitsize(20); dot((0,0)); dot((1,0)); dot((2,0)); dot((3,0)); dot((4,0)); dot((0,1)); dot((1,1)); dot((2,1)); dot((3,1)); dot((0,2)); dot((1,2)); dot((2,2)); dot((0,3)); dot((1,3)); dot((0,4));[/asy]
(A) 0(B) 1(C) 5!⋅4!⋅3!⋅2!⋅1!(D) 15!5!⋅4!⋅3!⋅2!⋅1!(E) 15!\text{(A)}\ 0\qquad\text{(B)}\ 1\qquad\text{(C)}\ 5!\cdot4!\cdot3!\cdot2!\cdot1!\qquad\text{(D)}\ \frac{15!}{5!\cdot4!\cdot3!\cdot2!\cdot1!}\qquad\text{(E)}\ 15!
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