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According to this answer, if six men are davening and ten men are present, the six can recite Kaddish and Kedushah. The case discussed is if the other four are not obligated because they already davened. Is it also true if one or more of the four is an onen? (The difference would be that those who already davened have fulfilled their obligation to pray, while the onen has no obligation at all.)

If so, this raises a question about women. As I understand it, women are not included in a minyan because they are exempt from the obligation of prayer. (My understanding is that for reading Megillat Esther, by contrast, women are included in a minyan because they are equally obligated.) So if the presence of an onen allows six men to say Kaddish and Kedushah, despite his having no obligation to pray, why would the presence of a woman not function similarly?

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An Onein does not count towards a Minyan. Rama writes (YD 341:1):

ומותר לילך לבית הכנסת בשבת. ואף בחול אין בו איסור רק מאחר שאסור להתפלל מה יעשה שם
He can go to synagogue on Shabbat, and even during the week there is no prohibition but since he can't pray, what would he do there?

Obviously helping make a Minyan wasn't an option. Many later authorities state that rule explicitly (e.g. Arukh HaShulchan YD 341:10).

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