Final answer:
To form a 4-person grievance committee with 3 members from Department A and 1 from Department B, there are 5720 possible combinations calculated using the formula for combinations: C(n, k) = n! / (k!(n - k)!).
Step-by-step explanation:
The question asks how many ways you can select a 4-person grievance committee consisting of 3 members from Department A with 12 people and 1 member from Department B with 26 people. This is a combination problem because the order in which the committee members are selected does not matter.
To find the total number of ways to form such a committee, we need to calculate the number of combinations for both departments. For Department A, we calculate the number of ways to select 3 people out of 12. This is a combination problem and can be represented by the formula C(n, k) = n! / (k!(n - k)!), where 'n' is the total number of people, 'k' is the number of people to choose, and '!' denotes factorial.
So for Department A, the combinations are C(12, 3). For Department B,where only 1 person is being selected, the combinations are C(26, 1).
The total number of possible committees is the product of the combinations from Department A and Department B:
Total combinations = C(12, 3) * C(26, 1)
Calculating these values, we get:
- C(12, 3) = 12! / (3!(12 - 3)!) = 220
- C(26, 1) = 26
Multiplying the two gives us:
Total combinations = 220 * 26 = 5720
Hence, there are 5720 ways to select a committee of 3 members from Department A and 1 member from Department B.