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1) The secretary problem does NOT assume a large number of candidates. In fact, your odds go down as the number of candidates go up.

2) The secretary problem DOES assume you can't go back once you've evaluated a candidate. This is not the case for prospective employees.

Edit: s/passed on/evaluated/

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I meant the 1/e neat solution (where the summation is replaced by an integral) assumes the large number. Otherwise, the sum can be evaluated directly, but no closed form solution exists.

I don't get your second statement, though, what do you mean by the "odds"? The 1/e solution is asymptotic.

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