Nine descendants of Imam Husain(a.s) are included in Ahlul-Bayt(a.s)

Only five members of Ahlul-Bayt were alive at the time of the Prophet  (PBUH&HF). They were Prophet Muhammad, Lady Fatimah, Imam Ali, Imam al-Hasan, and Imam al- Husain. They were mentioned as Ahlul-Bayt by the Prophet (PBUH&HF) and the most important Sunni  collections testify to this fact.

However the nine descendants of Imam al-Husain were not alive at that time so that the Prophet could not cover them by his mantle! But the Prophet did, in fact, mention their names and their numbers.

 Let us review some traditions from Sihah Sittah:

The Prophet (PBUH&HF) said: "al-Mahdi is one of us Ahlul-Bayt."

Sunni reference: Sunan Ibn Majah, v2, Tradition #4085

also:

The Prophet (PBUH&HF) said: "The Mahdi will be of my family, of the descendants of Fatimah (the Prophet's daughter).

Sunni references:
Sunan Abi Dawud, English version, Ch. 36, Tradition #4271 (narrated by Umm Salama, the wife of the Prophet)
Sunan Ibn Majah, v2, Tradition #4086
al-Nisa'i and al-Bayhaqi, and others as quoted in:
al-Sawa'iq al-Muhriqah, by Ibn Hajar al-Haythami, Ch. 11, section 1, p249

By the above traditions, the Prophet extended Ahlul-Bayt up to Imam al-Mahdi (AS). So Ahlul-Bayt are not just those five, and Imam al-Mahdi is the last member of Ahlul-Bayt, but he was not born at the time of the Prophet so that he could take him into the Cloak as well!

Also the messenger of Allah said:

"There shall be twelve Imams/Caliphs/Amirs for my nation"

Sunni references:
Sahih al-Bukhari, Arabic-English, v9, Tradition #329;
Sahih Muslim, English version, Chapter DCCLIV, v3, pp 1009-1010, Traditions #4476 -->
#4483;
Sunan Abi Dawud, v2, p421 (three traditions);
Sahih al-Tirmidhi, v4, p501;
Musnad Ahmad Ibn Hanbal, v5, p106;
Others such as al-Tiyalasi, Ibn al-Athir, etc.

These 12 Imams will cover till the day of resurrection as Sahih Muslim testifies. The last of them is surely Imam al-Mahdi (AS) who will appear in the last days and who is also from Ahlul-Bayt as the above tradition specified. There are other traditions in the Sunni collections in which the Prophet (PBUH&HF) has even mentioned the name of all these twelve individuals one by one. (see Yanabi' al- Mawaddah, by al-Qundoozi al-Hanafi).