Regarding a lack of Mehadrin; the Meiri, Shiltei Giborim and Magen Avraham all write that it is only necessary for adult children to light and not minors. There is no need to indicate the total number of people in the house to fulfill Mehadrin, only those obligated. The Mikraei Kodesh quoted above suggests that the same exemption should apply to girls and women.
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