Tony, so good you checked in here. Most people don't know this: The Kearsarge Pass trailhead has a daily quota of 60 hikers, and only 36 are reservable. The other 24 are held back for walk-in requests. Those walk-in permits become available at ANY Inyo ranger station (Lee Vining, Mammoth Lakes, Bishop and Lone Pine) at 11 AM the day BEFORE the date-of-entry on the trail.
If your friends can get to a ranger station and be in line at 11 AM, they are sure to get a permit. Also, since there are so many reservable, there are bound to be no-shows on the hike day, too. The no-shows are made available on the date-of-entry at 11 AM -- a little late to start and make it over to the other side of the pass, but it is entirely possible.
And finally, a few good people will log on to recreation.gov and cancel their reserved permits if they can't go, so watch online, especially the week before the hike, and some may become available.
You can find the link to the PDF file showing the quotas on this Inyo page:
Recreation Passes & PermitsHere's
the rec.gov link for Kearsarge Pass for your dates. Bookmark it, check it often.