In the state with the highest number of schools, how many institutions have a percentage of no less than 90 of undergraduates who attend full-time? List all of the institutions' names.
highest number of schools refers to MAX(schools_count); percentage of no less than 90 of undergraduates who attend full-time refers to ft_pct > 90; institutions' names refers to chronname;
SELECT COUNT(t1.unitid), t1.chronname FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON t1.state = t2.state WHERE t1.ft_pct > 90 ORDER BY t2.schools_count DESC LIMIT 1