Answer:
23.63% chance that exactly three is elderly
Explanation:
The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:

In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:
101 total people means that

Sample of 6 means that

66 elderly means that

If you talked to six random people there, what is the percent chance that exactly three is elderly?
This is P(X = 3). So


0.2363*100% = 23.63%
23.63% chance that exactly three is elderly