The track team gives awards for first, second, and third place runners. There are 10 students from school cap A and 12 students from school cap b competing. Which expression represents the probability that all three awards will go to a student from school cap b ?

Because first, second, and third place are distinct awards, order matters. There are 22 students total, so there are 22P3 possible ordered outcomes for the awards. For all three winners to be from school B, the choices are 12 students for first, then 11 for second, then 10 for third, giving 12P3 favorable outcomes. Thus the probability is 12P3 / 22P3, which is choice A.

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