Awizard has five friends. during a long wizards' conference, it met any given friend at dinner 10 times, any given pair of friends five times, any given threesome of friends three times, any given foursome two times, and all five friends together once. if in addition it ate alone six times, determine how many days the wizards' conference lasted.

i know the answer is 27 days, i just don't understand how to get that answer using inclusion/exclusion