Rob is preparing a report for his employer $,$ the employer will eventually deliver to federal aviation administration. First, report must be approved by Rob$$s group leader $,$ departmental head $,$ divisional chief $($in that order$).$ Rob knows from experience that $3$ managers act independently $.$ He also know that group leader approves $85\%$ of his reports $,$ his departmental head approves $80\%$ of his reports, and his division chief approves $82\%$ of his reports.

What is the probability that first version of Rob$$s report is submitted to FAA

a

$\mathrm{.}5576$

b

$0\mathrm{.}75$

c

$0\mathrm{.}8$