The one lonely man would most likely be killed off during the time when the most women had their time of the month...
I won't go into detail on the opposite vault
Due to the obvious nature of the male gender, their jealousy drove them to control the only female left. One night, while she was asleep, the Overseer came to kill her, to stop all the conflict. However, five suitors also snuck in, and instigated a riot. It killed off the only female, the Overseer, and an approximate 98% of the Vault in general.
And for the record, this is not canon. This is my take on Vault 68.