Answer :
To answer the question, we must first determine the total number of people in the sample space and the number of men within this group. However, since you haven't provided this information, I will guide you with a general approach on how to calculate the probability under the assumption that you have the necessary data.
Let's assume there are `N` total people, and out of those, there are `M` men. You want to find the probability that all five doses of medication are given to men.
The probability of selecting a man for the first dose is `M/N`.
After giving out the first dose, we have one less man and one less person overall, so the probability of giving the second dose to a man is `(M-1)/(N-1)`.
We continue this process, reducing the number of men and the total number of people by one each time, so the probabilities for the third, fourth, and fifth doses become `(M-2)/(N-2)`, `(M-3)/(N-3)`, and `(M-4)/(N-4)` respectively.
The probability of selecting five men consecutively is found by multiplying these individual probabilities:
P(five men) = `P(first man)` × `P(second man)` × `P(third man)` × `P(fourth man)` × `P(fifth man)`
P(five men) = `(M/N)` × `(M-1)/(N-1)` × `(M-2)/(N-2)` × `(M-3)/(N-3)` × `(M-4)/(N-4)`
This gives us the probability of selecting five men in a row from a group of `N` people with `M` men.
To give you the exact probability, plug in the values for `M` (number of men) and `N` (total number of people), calculate the product, and if required, round it to 3 decimal places or simplify the fraction.
Remember, this calculation is valid only if `M` ≥ 5, because we cannot give five doses to men if there are fewer than five men to begin with.
