Final answer:
The question asked for the number of possible blood donor combinations from a group of five potential donors. By using combination formulas, the sum is 31 possible combinations, which is not among the provided options.
Step-by-step explanation:
The student's question is about calculating the total number of possible blood donor combinations from a group of five potential donors - A, B, C, D, and E. Given that we are looking for combinations and not permutations, each selection is unique irrespective of order; thus, we use the combinations formula which is nCr = n! / (r!(n - r)!), where n is the total number of items, r is the number of items to choose, n! is the factorial of n, and r! is the factorial of r. In this case, the students may take any number of potential donors, so the total number of combinations would be the sum of combinations taken one at a time, two at a time, ... up to five at a time.
To find this, we sum up the combinations C(5,1) + C(5,2) + C(5,3) + C(5,4) + C(5,5), which are 5 + 10 + 10 + 5 + 1 = 31 possible donor combinations. Therefore, the correct answer is not listed among the options provided a) 5 b) 10 c) 15 d) 20, so the student should be aware that a mistake might have been made in the question or in the answer choices provided.