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This problem trains for: SAT-I, AMC-8, GMAT.

Schmendrick the magician draws at least one red marble whenever he pulls blindfolded five balls out of a bag of multicolored marbles. If there are ten red marbles in the bag, how many marbles are there that are not red?

(characters from Peter Beagle's "The Last Unicorn")

There are only four marbles that are not red. Otherwise, there would be some non-zero probability for the magician to pull out five marbles that are not red. Since this probability is exactly zero, that means there are only four such marbles.