Step-by-step Solution:

Concept: The number of elements in the power set of any set \( A \) is \( 2^n \), where \( n \) is the number of elements of the set \( A \). Calculation: Given, set \( S = \{ 2, \{1, 4\} \} \), Number of elements in set \( S = 2 \), \[ \therefore \text{The number of elements in the power set } P(S) = 2^2 = 4 \] Hence, option (2) is correct.