Final answer:
The problem is to calculate the number of possible committees of 4 people with at least 2 housekeepers from a group of 8 housekeepers and 5 maintenance workers, which is a combinatorics problem in mathematics.
Step-by-step explanation:
The question involves determining the number of possible committees that can be formed with certain restrictions, which is a combinatorics problem. Particularly, it's about choosing a committee of 4 people from 8 housekeepers and 5 maintenance workers with the constraint that there must be at least 2 housekeepers in the committee. The solution will require calculating combinations with various selections of housekeepers and maintenance workers.
To solve this, we need to consider different scenarios: selecting exactly 2 or 3 housekeepers (since selecting 4 would not leave room for a maintenance worker, which seems to be implied as a requirement). For each case, we calculate the number of ways to choose the housekeepers from the available 8, and the remaining committee members from the maintenance workers. We use the combination formula, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes the factorial of a number.
- Choosing exactly 2 housekeepers: C(8, 2) * C(5, 2)
- Choosing exactly 3 housekeepers: C(8, 3) * C(5, 1)
After calculating these combinations, we add them together to find the total number of possible committees.