In a race where 12 cars are running, the chance that car X will win is 1/6, that Y will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win. Options.
A) 1 / 140  B) 1 / 180  C) 27 / 410  D) 47 / 120  E) 57 / 120

Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d"
Answer: D