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In how many ways can five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians wait in line if no two Martians stand together?

What is throwing me off is the addition of another group - if it was just Martians and Vesuvians it would be easy. My guess is P(10,5) = (10*9*8*7*6)

Am I correct or did I mess this up?