As-salāmu ʿalaykum السَّلَامُ عَلَيْكُم
UDHIYAH FOR ENTIRE FAMILY.
Sahih Muslim 1967
The Book of Sacrifices, Book 35, Hadith 28
One sheep is sufficient as udhiyah for one man and his family and whoever he wants among the Muslims. ‘Aishah (may Allah be pleased with her) said that the Prophet (peace and blessings of
Allah be upon him) ordered that a ram with black legs, black belly and black (circles) around theeyes should be brought to him, so that he could sacrifice it.
'A'isha reported that Allah's Messenger (ﷺ) commanded that a ram with black legs, black belly and black (circles) round the eyes should be brought to him, so that he should sacrifice it. He said to 'A'isha: Give me the large knife, and then said: Sharpen it on a stone. She did that. He then took it (the knife) and then the ram; he placed it on the ground and then sacrificed it, saying: Bismillah, Allah-humma Taqabbal min Muhammadin wa Al-i-Muhammadin, wa min Ummati Muhammadin (In the name of Allah," O Allah, accept [this sacrifice] on behalf of Muhammad and the family of Muhammad and the Umma of Muhammad" ). Sahih Muslim 1967,
Abu Ayyub al-Ansari (may Allah be pleased with him) said: “At the time of the Prophet (peace and blessings of Allah be upon him), a man would sacrifice a sheep on behalf of himself and his household, and they would eat some and give some to others.” (Narrated by Ibn Majah and by alTirmidhi, who classed it as sahih. Also classed as sahih by al-Albani in Sahih al-Tirmidhi, 1216)
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 descendents of his father, grandfather and great-grandfather.
One-seventh of a camel or cow is equivalent to one sheep. If a man sacrifices one-seventh of a camel or cow on behalf of himself and his family, that is sufficient. Prophet Muhammad (peace and blessings of Allah be upon him) said that one-seventh of a camel or cow takes the place of a sheep
in the case of the hadiy (sacrifice offered during Hajj). So, this applies also to the udhiyah because there is no difference between the udhiyah and the hadiy in this regard