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

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Senior Manager
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A certain law firm consists of 4 senior partners and 6 [#permalink]

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14 May 2006, 05:42
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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 number of the group is a senior partner? (Two groups are considered different if at least one group member is different).

A. 48
B. 100
C. 120
D. 288
E. 600
Director
Joined: 16 Aug 2005
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14 May 2006, 13:24
I got this question in my GMATPrep exam today and got it right

B
Senior Manager
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14 May 2006, 20:37
Hey Prof is my approach correct? Thank you.
GMAT Club Legend
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14 May 2006, 20:42
Combis:

3 senior partner ---> # of ways = 4C3 = 4
2 senior partner + 1 junior partner ---> # of ways = 4C2*6C1 = 6*6 = 36
1 senior partner + 2 junior partner ---> # of ways = 4C1*6C2 = 4*15 = 60

Total = 4+36+60 = 100 groups
GMAT Club Legend
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14 May 2006, 20:44
M8 wrote:
Guys what about 10C3 - 4C1*6C1?

What is your basis for picking 4C1 and 6C1. You're just picking 1 senior partner and 1 junior partner, so you'll still be one man short.

The correct method should be 10C3 - 6C3 = 120-20 = 100. We use 6C3 because 3 junior partners in the group is an illegal condition.
VP
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15 May 2006, 17:34
M8 wrote:
Guys what about 10C3 - 4C1*6C1?

=10C3 - 4C1*6C1 = 120 - 24 = 96 is not correct because 4C1*6C1 means you are selecting each senoir and junior from 4 seniors and 6 juniors. why should we choose 2 (s+j) from 10?

you can do as deowl did.

=10C3 - 6C3
=120-20
=100
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