There are $$10$$ prizes, five A's, three B's, and two C's, placed in identical sealed envelopes for the top $$10$$ contestants in a mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the $$8th$$ contestant goes to select the prize, the probability that the remaining three prizes are one A, one B and one C is

Question

Infinity Learn · Accepted Answer

$$n(S)=10C7=120n(E)=5C4$$×$$3C2$$×$$2C1$$∴ $$P(E)=5$$×$$3$$×$$2120=14$$

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