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How many ways are there in which 2 purple stones, 1 yellow stone, 2 orange stones,...

How many ways are there in which 2 purple stones, 1 yellow stone, 2 orange stones, and 2 red stones can be placed on a 10x10 chessboard so that no two stones are in the same row and no two stones are in the same column. Please ignore symmetries, so that there are 4 ways of placing a stone on a corner of the chessboard, not 1 way. Show all work and write down the final expression (with explanations) whose value gives the correct answer. You do not have to calculate it numerically.

Math   Statistics-And-Probability   
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