# Chair Placement

I have 3 chairs to place within 8 spots. All three of my chairs come in 4 different colors.

Can I represent the number of possible placements as:

${24}\choose{3}$

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Question not clear. Can you distinguish among chairs of the same color? Do you have to use exactly one of each of the three chairs? –  Gerry Myerson Jan 16 '12 at 21:54
Yes, you can distinguish. Apologies. You have a red/green/blue/orange stool, a red/green/blue/orange couch, and a red/green/blue/orange crate. You MUST place exactly one stool, exactly one couch, and exactly one crate (each into one of the 8 positions). They cannot reside in the same position. –  sdasdadas Jan 16 '12 at 21:56

OK, then choose a stool (4), a couch (4), and a crate (4), so $4\times4\times4=64$ ways to choose the furniture. Then put the stool somewhere (8), the couch somewhere (7), the crate somewhere (6), so $8\times7\times6=336$ ways to places the chosen furniture. All told, $64\times336$.