Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2018	Oct. 01, 2017	Oct. 02, 2016
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, amortization expense	$ 186.5	$ 57.5	$ 57.3
Gross carrying amount	1,182.2	409.0
Accumulated amortization	(371.0)	(194.8)
Net Carrying Amount	811.2	214.2
Acquired and reacquired rights [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,081.7	328.8
Accumulated amortization	(320.1)	(154.2)
Net Carrying Amount	761.6	174.6
Acquired trade secrets and processes [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6	27.6
Accumulated amortization	(16.5)	(13.7)
Net Carrying Amount	11.1	13.9
Trade Names, trademarks and patents [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	33.0	31.5
Accumulated amortization	(19.5)	(17.6)
Net Carrying Amount	13.5	13.9
Licensing agreements [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	14.3	14.4
Accumulated amortization	(5.1)	(3.8)
Net Carrying Amount	9.2	10.6
Other finite-lived intangible assets [Member]
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	25.6	6.7
Accumulated amortization	(9.8)	(5.5)
Net Carrying Amount	$ 15.8	$ 1.2