a method of determining the number of secretaries to be selected

One of the most appropriate suspension issues is the selection of secretaries, but how should we decide the number to postpone?
Description of Wikipedia is difficult for me.

Additional
I was able to get the best value using the method you answered.
However, there were times when the price was not good, so I looked it up again and found out that
It seems that there is a way to maximize expectations for similar problems.
I looked at the formula, but in the end, I couldn't understand the specific calculation method, so I couldn't check it.
I don't mind a small number, so please tell me how to calculate it.

Formula I didn't know how to calculate

If the relative ranking of the i-th interview is r_i or higher, we will postpone it unless we are likely to adopt it

Equation I didn't know how to calculate
Algorithmic Dictionary Kyoritsu Publishing (1994/08) Page 646

algorithm

2022-09-30 20:31

1 Answers

If the number of applicants is n and large enough

If the number of people to send off is set to (n/e), the probability of hiring the best secretary is greatest.
The probability is 1/e.

If you set the number of people to (n/e), the probability of hiring the best secretary is greatest.

The probability is 1/e.

That's the solution to the secretarial selection problem.

The e used here is called the Napier number, Euler number, natural logarithmic bottom, etc., and its value is 2.718281828459045... (abbreviated below). e is an irrational number, just like the circumference, so the number below the decimal point continues indefinitely.

The reason for this result is explained in Wikipedia, but I think it is difficult to understand without knowledge of probability and calculus.However, you can easily calculate how many people you need to send off with a calculator.

For example, if there are 100 applicants, the number of applicants to be sent is 100/2.71824 = 36.7885 ... so 37 people (round off as it is not divisible). Then, you can choose someone better than any of the 37 people you saw off.

It's practically practical to say, "If you see more than one-third of the applicants off and the best person you've seen off, you'll choose that person."

2022-09-30 20:31

If you have any answers or tips

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