[Machine] From his grandfather Abdullah bin Hisham, who had witnessed the Prophet ﷺ , his mother Zainab bint Hameed took him to the Messenger of Allah ﷺ when he was young. The Prophet ﷺ wiped his head and prayed for him saying, "The Messenger of Allah ﷺ used to sacrifice one sheep on behalf of his entire family." All of these hadiths are authentic in terms of their chains of narrators regarding the permissibility of offering one sheep as a sacrifice on behalf of a group that is too numerous to count, contrary to those who assume that it is only permissible for an individual. There are narrations that indicate the permissibility of offering a sacrifice on behalf of the deceased as well.
عَنْ جَدِّهِ عَبْدِ اللَّهِ بْنِ هِشَامٍ وَكَانَ قَدْ أَدْرَكَ النَّبِيَّ ﷺ ذَهَبَتْ بِهِ أُمُّهُ زَيْنَبُ بِنْتُ حُمَيْدٍ إِلَى رَسُولِ اللَّهِ ﷺ وَهُوَ صَغِيرٌ فَمَسَحَ رَأْسَهُ وَدَعَا لَهُ قَالَ «كَانَ رَسُولُ اللَّهِ ﷺ يُضَحِّي بِالشَّاةِ الْوَاحِدَةِ عَنْ جَمِيعِ أَهْلِهِ» هَذِهِ الْأَحَادِيثُ كُلُّهَا صَحِيحَةُ الْأَسَانِيدِ فِي الرُّخْصَةِ فِي الْأُضْحِيَّةِ بِالشَّاةِ الْوَاحِدَةِ عَنِ الْجَمَاعَةِ الَّتِي لَا يُحْصَى عَدَدُهُمْ خِلَافَ مَنْ يَتَوَهَّمُ أَنَّهَا لَا تُجْزِئُ إِلَّا عَنِ الْوَاحِدِ وَقَدْ رُوِيَتْ أَخْبَارٌ فِي الْأُضْحِيَّةِ عَنِ الْأَمْوَاتِ صحيح