In this paper, we investigate some transitivity action properties of the cartesian product of the alternating group \(A_{n}(n \geq 5)\) acting on a cartesian product of ordered sets of triples using the Orbit-Stabilizer Theorem by showing that the length of the orbit \((p, s, v) \text { in } A_{n} \times A_{n} \times A_{n},(n \geq 5)\) acting on \(P^{[3]} \times S^{[3]} \times V^{[3]}\) is equivalent to the cardinality of \(P^{[3]} \times S^{[3]} \times V^{[3]}\) to imply transitivity.
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