Mastermind Permutations

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?

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1 Answer
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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.