Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:

So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:

Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:

So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get:

The answer is x=0 I believe because it is the only logical area
Not sure if this is right or not, but I chose 125.11 after I typed in the equation, haven’t used R-value at all. Will comment if correct — APEX
Answer:
a) F (A , B,C)(a,b,c) = abc
b) Answer is in derivative
Step-by-step explanation:
Hence area is maximum x=6
For ( a,b,c) ∈ (0,1)
We have that
F A, B,C (a,b,c) = A≤ a , B≤ b , C≤c
=P (A≤a) P (B≤b) P (C≤c)
A , B, C ≈ unit (0,1) we have that
P (A≤a) =a
P (B≤b) =b
P (C≤c)=c
Thus
F (A , B,C)(a,b,c) = abc
b) Answer is in derivative