Dora, I think you clicked the "Italics" button instead of the "Code" button in your message editor.
When you click a commandButton or commandLink, an HTML FORM submit is issued. In HTML, every control within that form has its value returned to the server as part of the form request (there's some qualification to that statement, but it's basically correct).
If you place 3 buttons on one form, the all the data items (dropdown SELECT values) still all get sent, regardless of which button was clicked, so what you want is actually automatic.
JSF, of course, is not straight HTML, so there's some additional considerations.
1. Since JSF validates requests, all controls on the submitted form must pass validation or the backing bean won't be updated. So either all 3 values will be set via the "set" methods of the backing bean or nothing will update and the action method will not be called.
2. You have 3 buttons, each of which has a corresponding action method. JSF will invoke the method that corresponds to the button that was clicked. All 3 values from the selectOneListbox controls will have been set, regardless of which button was clicked, however.
Other than that, the only other consideration is that you're giving your backing bean instance name an initial capitalized letter. By convention, you shouldn't do that for instances, only for Classes. When you use JSF2 annotations, the generated instance name will reflect that convention automatically.
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