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Goodwill and Other Intangible Assets - Changes in Carrying Amounts of Goodwill by Segment (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Oct. 31, 2018	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2017
Goodwill [Roll Forward]
Beginning balance		$ 1,834.8	$ 1,864.2
Purchase price adjustments			(6.2)
Reallocation		0.0
Foreign currency translation		0.6	(2.8)
Impairment loss		0.0	(20.3)	$ 0.0
Ending balance	$ 1,834.8	1,835.4	1,834.8	1,864.2
Business & Industry
Goodwill [Roll Forward]
Beginning balance		527.9	529.9
Purchase price adjustments			(0.9)
Reallocation		45.7
Foreign currency translation		0.3	(1.1)
Impairment loss			0.0
Ending balance	527.9	573.9	527.9	529.9
Aviation
Goodwill [Roll Forward]
Beginning balance		124.9	124.8
Purchase price adjustments			0.4
Reallocation		0.0
Foreign currency translation		0.1	(0.2)
Impairment loss			0.0
Ending balance	124.9	125.0	124.9	124.8
Technology & Manufacturing
Goodwill [Roll Forward]
Beginning balance		407.2	409.3
Purchase price adjustments			(2.1)
Reallocation		0.0
Foreign currency translation		0.0	0.0
Impairment loss			0.0
Ending balance	407.2	407.2	407.2	409.3
Education
Goodwill [Roll Forward]
Beginning balance		557.4	561.3
Purchase price adjustments			(3.8)
Reallocation		1.2
Foreign currency translation		0.0	0.0
Impairment loss			0.0
Ending balance	557.4	558.6	557.4	561.3
Technical Solutions
Goodwill [Roll Forward]
Beginning balance		158.7	180.0
Purchase price adjustments			0.4
Reallocation		11.8
Foreign currency translation		0.3	(1.5)
Impairment loss	(20.3)		(20.3)
Ending balance	158.7	170.7	158.7	180.0
Healthcare
Goodwill [Roll Forward]
Beginning balance		58.7	58.9
Purchase price adjustments			(0.2)
Reallocation		(58.7)
Foreign currency translation		0.0	0.0
Impairment loss			0.0
Ending balance	$ 58.7	$ 0.0	$ 58.7	$ 58.9