Responding to this issue, Sheikh Muhammad Salih Al-Munajjid, a prominent scholar and author, said:
“Give me the knife,”“In the name of Allah, O Allah, accept (this sacrifice) on behalf of Muhammad and the family of Muhammad and the Ummah of Muhammad.”
If a man sacrifices a single sheep or goat on behalf of himself and his family, that will suffice for everyone he intended of his family, whether living or deceased. If he did not intend anything specific, then it includes all those who are included in this word (family or household), either customarily or linguistically.
Customarily it refers to all those whom he supports of wives, children, and relatives; linguistically it includes all those who are related to him of his own children and the descendants of his father, grandfather, and great-grandfather.
One-seventh of a camel or cow is equivalent to one sheep. Hence, if a man sacrifices one-seventh of a camel or cow on behalf of himself and his family, that is sufficient because the Prophet (peace and blessings be upon him) said that one-seventh of a camel or cow takes the place of a sheep in the case of the hadi (sacrifice offered during Hajj), so that applies also to the udhiyah because there is no difference between the udhiyah and the hadi in this regard.
If two or more people buy a sheep and sacrifice it, that is not sufficient, because no such thing has been narrated in the Qur’an and Sunnah. Similarly, if eight or more people share one camel or one cow, that is not sufficient (but it is permissible for seven people to share a camel or cow), because acts of worship are as prescribed in the Qur’an and Sunnah and are not subject to personal opinion; it is not permissible to go beyond the set limits with regard to how much is to be done or the way in which it is to be done. This does not have to do with including others in the reward because it was narrated that there is no limit to the number of people on whose behalf the sacrifice may be offered.