From IMDb:

The world is destroyed when American kids accidentally set off a nuclear missile, causing the Russians to counterattack. Only six people are left in the US: Mark, the narrator, an ex-school teacher; Alice, a feminist; Curtis, a yuppie stock broker; Jack, a homeless person; Frederick, a black pathologist; and Suzanne, a sexy ditz.
 
https://www.imdb.com/title/tt0103583