According to Graicuna's formula of span of management, if a superior has three subordinates, what number of cross-relationships would be?
six
V. A. Graicunas studied how the relationships a superior must handle grow as the number of subordinates rises, and he distinguished three kinds of relationship: direct single relationships (superior with each subordinate one to one), direct group relationships (superior with subordinates in groups), and cross relationships (subordinates interacting with one another).
The number of cross relationships alone - those that run between the subordinates themselves - is given by the formula \(n(n-1)\), where n is the number of subordinates.
Substituting n = 3 gives cross relationships = \(3 \times (3-1) = 3 \times 2 = 6\).
(The much larger total of all three kinds together would use \(n\left(2^{\,n-1} + n - 1\right)\), but the question asks only for the cross relationships.)
Hence the number of cross-relationships is six.
