"Parents' committee" is right. PARENT'S is the possessive form of PARENT, so it means "of, or belonging to, a/the PARENT" (singular). PARENTS' is the possessive form of PARENTS, so it means "of, or belonging to, the PARENTS" (plural).
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James MSome Americans in 2012 feel that apostrophes should be used only for real possession.Some Americans in 2012 feel that apostrophes shouldn't be used at all! :-)
James MDo not add an apostrophe to a word ending in s when it is used primarily in a descriptive sense: a teachers college; a writers guideI see. I personally don't like the rule, whatever rationale is behind it (and they don't state any), but that's a pretty formal source, so thanks for the info!
anonymous parents' committee or parent's committee which is the correct one