Whenever the Prophet ﷺ set out on a journey, he would draw lots among his wives.
أن النبي ﷺ كان إذا خرج أقرع بين نسائه.
No references are available.
Bukhari reported it in the Book of Marriage (5211), and Muslim in the Book of the Virtues of the Companions (2445), both from the hadith of Abu Naeem, who said, "Abdul-Wahid bin Ayman narrated to us," who said, "Ibn Abu Mulayka narrated to me, from Qasim bin Muhammad, from Ayesha," and he related it as part of a long hadith.