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Question

The required no of ways

$ = {\,^{10}}{{\rm{C}}_3} + {\,^{19}}{{\rm{C}}_4} + {\,^{10}}{{\rm{C}}_5} +  \ldots  + {\,^{19}}{{\rm{C}}_6} + {\

Vedclass · Accepted Answer

$912$

Vedclass · Answer

The required no of ways

$ = {\,^{10}}{{\rm{C}}_3} + {\,^{19}}{{\rm{C}}_4} + {\,^{10}}{{\rm{C}}_5} +  \ldots  + {\,^{19}}{{\rm{C}}_6} + {\,^{10}}{{\rm{C}}_7}$

$ = {2^{10}} - \,\left( {^{10}{{\rm{C}}_0} + {\,^{10}}{{\rm{C}}_1} + {\,^{10}}{{\rm{C}}_2} + {\,^{10}}{{\rm{C}}_8} + {\,^{10}}{{\rm{C}}_9} + {\,^{10}}{{\rm{C}}_9}} \right)$

$=2^{10}-2(1+10+45)=912$

A company has $10$ employes. The company has decided to form a team including atleast three employes and also excluding atleast three employes. Then the number of ways of forming the team is

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