Explanation:

To find the number of ways in which three people, each throwing a single die once, can make a score of 11, we can use the concept of generating functions.

Generating Function:
A generating function is a formal power series that encodes information about a sequence of numbers. In this case, we can represent the score of each person throwing a die as a power series.

Step 1: Representing the Score of Each Person:
Let's represent the score of each person as a power series, where the coefficient of x^k represents the number of ways to get a score of k.

Person 1: x + x^2 + x^3 + x^4 + x^5 + x^6
Person 2: x + x^2 + x^3 + x^4 + x^5 + x^6
Person 3: x + x^2 + x^3 + x^4 + x^5 + x^6

Step 2: Multiplying the Generating Functions:
To find the generating function for the combined score of all three people, we multiply the generating functions of each person.

(x + x^2 + x^3 + x^4 + x^5 + x^6) * (x + x^2 + x^3 + x^4 + x^5 + x^6) * (x + x^2 + x^3 + x^4 + x^5 + x^6)

Step 3: Simplifying the Generating Function:
Now, we need to simplify the generating function by multiplying the terms. This can be done by multiplying the coefficients of the same powers of x.

The coefficient of x^11 in the simplified generating function will represent the number of ways to get a total score of 11.

Step 4: Finding the Coefficient of x^11:
To find the coefficient of x^11, we need to consider all possible combinations of terms from the three generating functions that multiply to give x^11.

In this case, the coefficient of x^11 is 27, which means there are 27 ways in which three people can make a score of 11 by throwing a single die once.

Therefore, the correct answer is option B, which is 27.