Summation of a Random Variable
Your outcomes are not the number of candidates but rather which candidates were hired: $\Omega = \{0,1\}^n$. Then you have $X_i(a_1, \dots, a_n) = a_i$ and $X(a_1, \dots, a_n) = \sum\limits_{i=1}^n X_i(a_1, \dots, a_n) = \sum\limits_{i=1}^n a_i$.