Andrew is a mid-level manager with three organizational levels above him and two below him.He has four analysts reporting directly to him.Using Graicunas's formula,calculate the total number of possible relationships between Andrew and his subordinates.
A)4
B)16
C)44
D)56
E)64

Question

Quizplus · Accepted Answer

Graicunas's formula for calculating the total number of possible relationships in a direct reporting scenario is given by: $V = n + n(n - 1) + \frac{n(n - 1)(n - 2)}{2}$, where $V$ is the total number of relationships and $n$ is the number of subordinates. For Andrew, $n = 4$, so $V = 4 + 4(4 - 1) + \frac{4(4 - 1)(4 - 2)}{2} = 4 + 12 + 12 = 28$. However, the correct formula for calculating the total number of relationships including direct, cross, and direct group relationships is $V = n + n(n - 1) + 2[n(n - 1)(n - 2)/3!]$, which simplifies to $V = n + n(n - 1) + n(n - 1)(n - 2)/3$. Substituting $n = 4$, we get $V = 4 + 4(3) + 4(3)(2)/3 = 4 + 12 + 8 = 24$. It seems there was a mistake in the calculation process described. The correct application of Graicunas's formula for the total number of relationships including direct, cross, and direct group relationships should indeed result in $V = 4 + 12 + 12 = 28$, but this does not match any of the provided options, indicating a misunderstanding in the explanation. The correct calculation using the standard formula $V = n + n(n - 1) + n(n - 1)(n - 2)/2$ for $n = 4$ actually results in $V = 4 + 12 + 12 = 28$, which still does not align with the provided options, suggesting an error in the initial explanation. The correct interpretation of Graicunas's formula and calculation should lead to the correct total number of relationships, which is not accurately reflected in the initial response. The correct answer, based on the standard interpretation of Graicunas's formula, should be recalculated or the correct formula and its application should be clarified to match the provided options.

Andrew Is a Mid-Level Manager with Three Organizational Levels Above