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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] New post 19 Nov 2007, 05:21
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Difficulty:

  25% (medium)

Question Stats:

74% (01:48) correct 26% (01:04) wrong based on 158 sessions
A firm has 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 at least one group member is different)

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

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-firm-has-4-senior-partners-and-6-junior-partners-how-many-106010.html
[Reveal] Spoiler: OA

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Re: PS - Combination [#permalink] New post 19 Nov 2007, 07:18
alimad 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)

48
100
120
288
600

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS


1Senior2Juniors + 2Seniors1Junior + 3Seniors =
4C1 * 6C2 + 4C2 *6C1 + 4C3
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Re: PS - Combination [#permalink] New post 19 Nov 2007, 07:24
alimad 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)

48
100
120
288
600

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS


Your method is correct but you have not considered the possibility of all the 3 members of the group being senior members.
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 [#permalink] New post 19 Nov 2007, 20:13
how about this approach:

# of teams with at least 1 senior = total # of teams - # of teams with 0 senior partners

total # = 10C3

# of teams with 0 seniors = 6C3

but this didnt give me the right answer .... what am i missing ?
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Re: PS - Combination [#permalink] New post 20 Nov 2007, 19:25
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GMATBLACKBELT wrote:
alimad 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)

48
100
120
288
600

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS


im really lost on this problem...


What really helps me in these type of problems is to approach the thought process like this:

1. What are the total # of combinations without any restrictions ?

2. What are the total # of combinations using the OPPOSITE of the restriction ?

3. The # of combinations with the restriction is the difference between 1 and 2

So, for this question, 1 would be 10C3. 2 would be 6C3, which gives the # of ways to pick 3 ppl out of the 6 junior partners, i.e. no seniors.

The final answer should be 10C3 - 6C3
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 [#permalink] New post 21 Nov 2007, 07:48
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Total no of groups of 3 members (including junior and senior) = 10C3
Total no of groups of 3 members (only juniors) = 6C3
Total no of groups of 3 members (at least 1 senior) = 10C3 - 6C3 = 120 - 20 =100
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Re: PS - Combination [#permalink] New post 23 Nov 2007, 23:26
pmenon wrote:
GMATBLACKBELT wrote:
alimad 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)

48
100
120
288
600

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS


im really lost on this problem...


What really helps me in these type of problems is to approach the thought process like this:

1. What are the total # of combinations without any restrictions ?

2. What are the total # of combinations using the OPPOSITE of the restriction ?

3. The # of combinations with the restriction is the difference between 1 and 2

So, for this question, 1 would be 10C3. 2 would be 6C3, which gives the # of ways to pick 3 ppl out of the 6 junior partners, i.e. no seniors.

The final answer should be 10C3 - 6C3


pmenon great explanation!! I totally lost this one.
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Re: PS - Combination [#permalink] New post 21 Feb 2008, 11:38
At least one = Total - none

At least one = 10C3 - none

None = 6C3

= 10C3 - 6C3
= 120 - 20 = 100
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Re: PS - Combination [#permalink] New post 21 Feb 2008, 11:47
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All possibilities = 10!/7!3! = 120

So the answer will be a fewer than 120; 48 is of course too few since it's less than half, so 100 looks good enough for me.
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Re: PS - Combination [#permalink] New post 05 Aug 2008, 00:06
But why 10C3 - 6C3?

Shouldn't it be 10P3 - 6P3

Bcoz the question mentions
(Two groups are considered different if at least one group member is different)

Am I missing something here...
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Re: PS - Combination [#permalink] New post 27 Sep 2009, 22:30
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)

48
100
120
288
600


Soln:
= 4C2 * 6C1 + 4C1 *6C2 + 4C3
= 100 ways
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Re: PS - Combination [#permalink] New post 16 Feb 2010, 12:32
alimad 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)

48
100
120
288
600

My take :

4C1 * 6C2 + 4C2 *6C1

pLEASE ADVICE. tHANKS


Ans = Total Comb - Comb with only junior partners = 10c3 - 6c3 = 100 (B)
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Re: A certain law firm consists of 4 senior partners and 6 [#permalink] New post 17 Jul 2013, 12:49
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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)

48
100
120
288
600


Another approach:

SSSS JJJJJJ

We have 4 seniors and 6 juniors.
We are asked for the nomber of groups of 3 in which at least 1 is a senior (1, 2 or 3 seniors in each group).
Considering that we have 3 types of groups:

Groups with 1 senior:
We take 1 senior out of 4 (C^4_1) and combine them with 2 juniors out of 6 (C^6_2):

C^4_1*C^6_2 = 4*15 = 60

Groups with 2 seniors:
We take 2 seniors out of4 (C^4_2) and combine them with 1 juniors out of 6 (C^6_1):

C^4_2*C^6_1 = 6*6 = 36

Groups with 3 seniors (and zero juniors):
We take 3 seniors out of 4 (C^4_3):

C^4_3 = 4

60 + 36 + 4 = 100
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Re: A certain law firm consists of 4 senior partners and 6 [#permalink] New post 17 Jul 2013, 13:49
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Maxirosario2012 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)

48
100
120
288
600


Another approach:

SSSS JJJJJJ

We have 4 seniors and 6 juniors.
We are asked for the nomber of groups of 3 in which at least 1 is a senior (1, 2 or 3 seniors in each group).
Considering that we have 3 types of groups:

Groups with 1 senior:
We take 1 senior out of 4 (C^4_1) and combine them with 2 juniors out of 6 (C^6_2):

C^4_1*C^6_2 = 4*15 = 60

Groups with 2 seniors:
We take 2 seniors out of4 (C^4_2) and combine them with 1 juniors out of 6 (C^6_1):

C^4_2*C^6_1 = 6*6 = 36

Groups with 3 seniors (and zero juniors):
We take 3 seniors out of 4 (C^4_3):

C^4_3 = 4

60 + 36 + 4 = 100


A firm has 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 at least one group member is different)
A. 48
B. 100
C. 120
D. 288
E. 600

Total # of different groups of 3 out of 10 people: C^3_{10}=120;
# of groups with only junior partners (so with zero senior member): C^3_6=20;

So the # of groups with at least one senior partner is {all} - {none}= {at least one} = 120-20 = 100.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-firm-has-4-senior-partners-and-6-junior-partners-how-many-106010.html
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Re: A certain law firm consists of 4 senior partners and 6   [#permalink] 17 Jul 2013, 13:49
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