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

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A certain law firm consists of 4 senior partners and 6 [#permalink]  31 Aug 2008, 11:03
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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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600
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Re: GMAT PREP Combinatorics Q [#permalink]  31 Aug 2008, 11:58
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lionheart187 wrote:
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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600

(4C1*6C2) * (4C2*6C1) * (4C3*6C0) = 60+36+4 = 100

What is OA?
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Re: GMAT PREP Combinatorics Q [#permalink]  31 Aug 2008, 12:17
leonidas wrote:
lionheart187 wrote:
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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600

(4C1*6C2) * (4C2*6C1) * (4C3*6C0) = 60+36+4 = 100

What is OA?

(4C1*6C2) + (4C2*6C1) + (4C3*6C0) = 60+36+4 = 100
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Senior Manager
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Posts: 350
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Re: GMAT PREP Combinatorics Q [#permalink]  31 Aug 2008, 12:22
GMAT TIGER wrote:
leonidas wrote:
lionheart187 wrote:
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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600

(4C1*6C2) * (4C2*6C1) * (4C3*6C0) = 60+36+4 = 100

What is OA?

(4C1*6C2) + (4C2*6C1) + (4C3*6C0) = 60+36+4 = 100

Oops!! Good catch GMAT TIGER.
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To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton

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Re: GMAT PREP Combinatorics Q [#permalink]  01 Sep 2008, 00:51
Bump for a little more clarification.
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Re: GMAT PREP Combinatorics Q [#permalink]  01 Sep 2008, 00:57
dominion wrote:
Bump for a little more clarification.

you need atleast one senior partner ( group can have one senior parter or two senior partner or three senior partners)
= 1 Senior 2 Juniors+ 2 Seniors 1 Junior + 3 Senior 0 Juniors
(4C1*6C2) + (4C2*6C1) + (4C3*6C0) = 60+36+4 = 100
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Re: GMAT PREP Combinatorics Q [#permalink]  02 Sep 2008, 10:07
lionheart187 wrote:
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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600

10C3 - 6C3 = 120-20 = 100
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Re: GMAT PREP Combinatorics Q [#permalink]  02 Sep 2008, 22:20
zoinnk wrote:
lionheart187 wrote:
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 least one group member is different.)

A)48
B)100
C)120
D)288
E)600

10C3 - 6C3 = 120-20 = 100

out of the box. nice.
Re: GMAT PREP Combinatorics Q   [#permalink] 02 Sep 2008, 22:20
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# A certain law firm consists of 4 senior partners and 6

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