A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners. Can be formed in which at least one member of the group is a senior partner(2 groups are considered different if least one group members is different)
answer: 100
law firm
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- jayhawk2001
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S = Senior Partner, J = Junior Partner
Possibilities are SJJ, SSJ and SSS
SJJ = 4C1*6C2 = 60
SSJ = 4C2 * 6C1 = 36
SSS = 4C3 = 4
Sum = 100
Possibilities are SJJ, SSJ and SSS
SJJ = 4C1*6C2 = 60
SSJ = 4C2 * 6C1 = 36
SSS = 4C3 = 4
Sum = 100
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Total ways in which 3 partners can be selected from a total of 10 members (6 junior and 4 senior), without restrictions = 10C3 = 120 ways
Total ways in which 3 partners can be selected from a total of 6 junior members (making sure that neither of the 3 chosen are senior partners = 6C3 = 20 ways
Hence groups of 3 partners in which atleast one is a senior partner = 120 - 20 = 100
Total ways in which 3 partners can be selected from a total of 6 junior members (making sure that neither of the 3 chosen are senior partners = 6C3 = 20 ways
Hence groups of 3 partners in which atleast one is a senior partner = 120 - 20 = 100