To determine the number of arrangements for 5 individuals in a linear formation, we apply the permutation principle. Permutation Formula Application The quantity of possible orderings for \( n \) unique items in a sequence is calculated using the factorial function: \[ P(n) = n! \] Given 5 people, \( n \) equals 5. We must compute \( 5! \). Calculation of \( 5! \) \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] Conclusion: There are \( 120 \) distinct arrangements for 5 people in a row, corresponding to option (1).