A permit for 8 could be tough. The weather is supposed to be nice the rest of the week and there is only a low chance of showers over the weekend which won't help your chances. Pack up and be ready to go. Check for cancellations later this week. Openings often appear a day or two ahead of time.
I'm not happy about being over the hill, but I am grateful there wasn't a cliff at the summit! - Frank and Ernest