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STEP I/2001/14

I/2001/14 – On the basis of an interview, the N candidates for admission to a college are ranked in order according to their mathematical potential. The candidates are interviewed in random order (that is, each possible order is equally likely).

Find the probability that the best amongst the first n candidates interviewed is the best overall.

Find the probability that the best amongst the first n candidates interviewed is the best or second best overall.

Verify your answers for the case N=4, n=2 by listing the possibilities.

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