Here's how to determine the formula:

* Thallium(III) indicates that thallium has a +3 charge (Tl³⁺).

* Sulfide refers to the sulfur anion, which has a -2 charge (S²⁻).

* To balance the charges, you need two thallium ions (2 x +3 = +6) and three sulfide ions (3 x -2 = -6).

Therefore, the formula is Tl₂S₃.