Goodwill and Other Intangible Assets - Changes in Carrying Amounts of Goodwill by Segment (Details) - USD ($)	3 Months Ended	12 Months Ended
	Apr. 30, 2020	Oct. 31, 2021	Oct. 31, 2020
Goodwill [Roll Forward]
Beginning balance		$ 1,671,400,000	$ 1,835,400,000
Acquisition		554,000,000.0
Foreign currency translation		3,400,000	(200,000)
Impairment loss	$ (163,800,000)	0	(163,800,000)
Ending balance		2,228,900,000	1,671,400,000
Business & Industry
Goodwill [Roll Forward]
Beginning balance		574,000,000.0	573,900,000
Acquisition		554,000,000.0
Foreign currency translation		1,800,000	100,000
Impairment loss			0
Ending balance		1,129,800,000	574,000,000.0
Technology & Manufacturing
Goodwill [Roll Forward]
Beginning balance		407,200,000	407,200,000
Acquisition		0
Foreign currency translation		0	0
Impairment loss			0
Ending balance		407,200,000	407,200,000
Education
Goodwill [Roll Forward]
Beginning balance		459,300,000	558,600,000
Acquisition		0
Foreign currency translation		0	0
Impairment loss	(99,300,000)		(99,300,000)
Ending balance		459,300,000	459,300,000
Aviation
Goodwill [Roll Forward]
Beginning balance		69,500,000	125,000,000.0
Acquisition		0
Foreign currency translation		400,000	0
Impairment loss	(55,500,000)		(55,500,000)
Ending balance		69,900,000	69,500,000
Technical Solutions
Goodwill [Roll Forward]
Beginning balance		161,500,000	170,700,000
Acquisition		0
Foreign currency translation		1,200,000	(300,000)
Impairment loss	$ (9,000,000)		(9,000,000.0)
Ending balance		$ 162,700,000	$ 161,500,000