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I'm looking for a way to calculate the probability to be able to get your holidays when you want based on:

  • There are $365$ days in the year
  • Weekends will be counted as normal days (to simplify)
  • You can take $20$ days holidays
  • There are $x$ number of persons taking $20$ days holidays and you can not take the same days

My guess is that for one person it will be $$\frac{(365-20)}{365}=0.945$$ and for $x$ number of persons will be $$\frac{(365-(20*x))}{365}$$. Is this correct?

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Let $x=$total employees.

Let $y=$number of employees who have already chosen their days.

The probability of any position in order of picking vacation days, i.e first, second, third... is $\frac{1}{x}$

The probability of getting the days you want is a function number of people who have picked before yourself.$$\frac{365-20*y}{365}$$ You had the right function, except the variable represents the number of people whom have already chosen vacation days, not the total amount of employees.

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    Thanks Nick for your answer. This formula could end up with negative values. Is it correct to say that when 20*y>365, then the probability is zero? – 2017-02-18
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    It is probably more likely you wont get a negative value, assuming the company didnt say everyone gets 20 days and there is like 20 employees. – 2017-02-18