Question

A pharmaceutical company recently hired 4 biologists, 6 chemists, 3 environmental scientists, and 2 economists for various upcoming projects. suppose that the company wants to form an interdisciplinary project group of 6 from these new hires to assess the potential environmental impact of developing a new experimental drug. which of the following gives the total number of project teams that contain at least 2 biologists?

a. P(2,2)P(13,4) / P(15,6)
b. 2/15
c. 1 - C(2,2)C(13,4) / C(15,6)
d. C(2,2)C(13,4) / C(15,6)

Answer 1

The total number of project teams containing at least 2 biologists from the given group of new hires can be calculated using combinations. By choosing 2 biologists and then the remaining 4 members, the correct number of teams is 4,290.

Step-by-step explanation:

The question is asking for the total number of project teams that could be formed from a group of new hires that contains at least 2 biologists. We can solve this by using combinations since the order of selection does not matter. We first choose 2 biologists out of the 4 available, and then we can choose the remaining 4 members of the project team out of the 13 remaining hires (6 chemists, 3 environmental scientists, and 2 economists).

The correct formula to calculate this would be using combinations: C(4,2) for choosing 2 biologists and C(13,4) for choosing the remaining 4 team members from the other hires, and then multiplying these two values together.

The formula is therefore:

C(4,2) × C(13,4)

We can then calculate the values:

C(4,2) = 4! / (2!(4-2)!) = 6

C(13,4) = 13! / (4!(13-4)!) = 715

Multiplying these together, we get:

6 × 715 = 4290

So, the total number of project teams that could be formed with at least 2 biologists is 4290.