law firm

[yvonne12]

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

[Tame the CAT]

4!/3!*6!/(2!4!)+4!/(2!2!)*6!/5!+4!

This gives 100

[jayhawk2001]

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

[Cybermusings]

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

[yvonne12]

oh, I didnt add the 3 senior. Although, the question specifically asked for at least 1 senior to be in the group?