"The committee needs to select someone for written the report before the meeting."

The correct option is "to write," as it properly fits the context of needing to select someone for the task of writing the report. The sentence should read: "The committee needs to select someone to write the report before the meeting," which indicates the action that needs to be performed. Writing and written do not fit grammatically in this context. The sentence is in present tense, so the verb should also be in present tense while 'wrote' is past form of 'write', hence cannot correct grammatically.