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Income Taxes (Summary of Activity Related to Unrecognized Tax Benefits) (Details) - USD ($)
$ in Millions
12 Months Ended
Oct. 03, 2021
Sep. 27, 2020
Sep. 29, 2019
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]      
Beginning balance $ 123.7 $ 132.1 $ 224.6
Increase related to prior year tax positions 4.8 11.1 3.8
Decrease related to prior year tax positions (11.9) (0.5) (75.3)
Increase related to current year tax positions 8.9 9.8 18.5
Decreases related to settlements with taxing authorities (4.4) 0.0 (16.4)
Decreases related to lapsing of statute of limitations (38.5) (28.8) (23.1)
Ending balance 82.6 123.7 132.1
Gross unrecognized tax benefits 82.6 123.7 132.1
Unrecognized tax benefits affecting the effective tax rate if recognized 62.8    
Interest and penalties expense/(benefit) recognized in income tax expense 4.6 (3.0) $ 2.8
Accrued interest and penalties $ 7.1 $ 13.0