How can a lottery be conducted among wives to determine who travels with the husband?

It is permissible for a man to travel alone without his wives, or to travel with all of them. However, if he wishes to travel with one of them, he must draw lots between them, or the wives must consent to one of them traveling, in accordance with the guidance of the Prophet, peace and blessings be upon him.

As for fairness in lodging overnight, it means that the husband stays with each wife for her entire night, and he does not enter upon her co-wife except for a need, a necessity, or with the permission of the wife whose night it is. He is obligated to make up the nights for those who missed them.

To draw lots, one can write "Does not travel" on three slips of paper and "Travels" on a fourth slip. Then, each wife picks a slip, and the one whose lot falls on "Travels" travels with him. Alternatively, they can agree on any other method of drawing lots that is agreeable to all of them.