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# A certain law firm consists of 4 senior partners and 6

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Manager
Joined: 02 Jul 2007
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A certain law firm consists of 4 senior partners and 6 [#permalink]  10 Sep 2007, 04:52
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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? (Two groups are considered different if at leats one group member is different)

A) 48
B) 100
C) 120
D) 288
E) 600
Manager
Joined: 02 Jul 2007
Posts: 112
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Got it, had trouble remembering how to set up these combination problems.

10C3-6C3 = 120-20=100

OA is 100
Intern
Joined: 26 Jul 2007
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Could you explain the logic behind this problem? I understand how the correct answer is arrived at, but I don't understand why we need to find how many ways you can take 10 things 3 at a time minus 4 things 1 at a time in order to get the correct answer. Thanks in advance.
Manager
Joined: 02 Jul 2007
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It took me almost a month to understand how to do these problems, but this site was litered with ideas how. It really helped.

The problem asks for how many goups with at least 1 senior partner. First find out how many total groups are possible (10C3) then subtract from that the number of possible groups that have no senior partner (6C3). You have to use combinations b/c there is nothing distiguishing one senior member for another, so you have to avoid double counting.

Hope that helps.
Intern
Joined: 26 Jul 2007
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It does; thanks very much.
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