Dots or Pegs?
Probability
Level
3
There are 5 yellow pegs, 4 red pegs, 3 green pegs, 2 blue pegs and 1 orange peg to be placed on a triangle peg board. In how many ways can the pegs can the pegs be placed such that no row or column contains two pegs of same color?
0
1
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1 solution
In each column, there must be one yellow peg. In particular, in the rightmost column, there is only one peg spot, therefore, a yellow peg must go there.
In second column from right, there are 2 spaces for peg. One of them is in the same row as the corner peg, so there is only one remaining choice left for the yellow peg in the column. By similar logic, we can fill in the yellow pegs as shown,
After this we can proceed to fill the whole pegboard, so there is only o n e arrangement of the pegs.