Recall that Mastermind codes consist of an ordered row of four colors. (For instance,
RED BLUE BLUE ORANGE is one code; BLUE RED BLUE ORANGE is a different
code.) There are six different colors to choose from. How many ways are there of
choosing a Mastermind code that uses the color orange exactly once?
You can place the orange in any of 44 slots. Then the question becomes, how many distinct codes can be formed from five colors in the remaining three slots; the answer is obviously 535^3. So the answer to your question is 500500.