One sacrifice is sufficient on behalf of all the members of a household, no matter how many of them there are.
Al-Tirmidhi (1505) narrated that ‘Ata’ ibn Yassaar said: I asked Abu Ayyoob: How was the sacrifice done at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him)? He said: A man would offer a sheep on behalf of himself and the members of his family, and they would eat some and feed others with some.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
It says in Tuhfat al-Ahwadhi:
This hadeeth clearly states that a single sheep is sufficient on behalf of a man and the members of his household, even if they are many, and that is correct.
Al-Haafiz ibn al-Qayyim said in Zaad al-Ma’aad: The teaching of the Prophet (peace and blessings of Allaah be upon him) was that a sheep is sufficient on behalf of a man and the members of his household, even if they are many in number.
Al-Shawkaani said in Nayl al-Awtaar: In fact a single sheep is sufficient on behalf of the members of a household, even if there are one hundred or more, as is indicated by the Sunnah. End quote.
Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’ (5/275):
There is no limit to how many people may share in the reward. The Prophet (peace and blessings of Allaah be upon him) offered a sacrifice on behalf of his entire ummah, and a man may offer a single sheep on behalf of himself and the members of his household, even if they are one hundred strong. End quote.
The Standing Committee was asked: There are twenty-two people in this family, and they have one income and one budget. On Eid al-Adha they offer a single sacrifice, and I do not know whether that is sufficient or whether they should offer two sacrifices?
If the family is big but they live in one house, one sacrifice is sufficient for them, but if they offer more than one sacrifice, that is better. End quote.
Fataawa al-Lajnah al-Daa’imah, 11/408.