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Severance (Details) - USD ($) $ in Millions	12 Months Ended
Severance (Details) - USD ($) $ in Millions	Oct. 02, 2020	Sep. 27, 2019	Sep. 28, 2018
Accrued Payroll and Related Expenses
Restructuring Reserve [Roll Forward]
Severance and Related Costs Accrual Beginning Balance	$ 11.9
Charges	145.8
Payments and Other	(36.7)
Severance and Related Costs Accrual Ending Balance	121.0	$ 11.9
COVID-Related Severance \| Cost of Services Provided and Selling and General Corporate Expenses
Restructuring Reserve [Roll Forward]
Charges	145.8
COVID-Related Severance \| Cost of Services Provided and Selling and General Corporate Expenses \| Corporate, Non-Segment
Restructuring Reserve [Roll Forward]
Charges	1.8
COVID-Related Severance \| Cost of Services Provided and Selling and General Corporate Expenses \| Food and Support Services - United States
Restructuring Reserve [Roll Forward]
Charges	51.8
COVID-Related Severance \| Cost of Services Provided and Selling and General Corporate Expenses \| Food and Support Services - International
Restructuring Reserve [Roll Forward]
Charges	87.3
COVID-Related Severance \| Cost of Services Provided and Selling and General Corporate Expenses \| Uniform
Restructuring Reserve [Roll Forward]
Charges	4.9
Employee Severance and Other Costs
Restructuring Reserve [Roll Forward]
Charges		18.7	$ 36.6
Employee Severance and Other Costs \| Accrued Payroll and Related Expenses
Restructuring Reserve [Roll Forward]
Severance and Related Costs Accrual Beginning Balance	11.9
Charges	0.0
Payments and Other	(9.4)
Severance and Related Costs Accrual Ending Balance	2.5	11.9
Employee Severance and Other Costs \| COVID-Related Severance \| Accrued Payroll and Related Expenses
Restructuring Reserve [Roll Forward]
Severance and Related Costs Accrual Beginning Balance	0.0
Charges	145.8
Payments and Other	(27.3)
Severance and Related Costs Accrual Ending Balance	$ 118.5	$ 0.0