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# A certain university will select 1 of 7 candidates eligible

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Joined: 22 Nov 2007
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A certain university will select 1 of 7 candidates eligible [#permalink]

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05 Jan 2008, 09:39
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Question Stats:

90% (00:38) correct 10% (00:47) wrong based on 386 sessions

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A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-university-will-select-1-of-7-candidates-eligible-103273.html
[Reveal] Spoiler: OA

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CEO
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05 Jan 2008, 09:48
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Expert's post
E

N=7C1*2C10=7*45=315
we use 2C10 rather than 2P10 because "2 of 10 candidates eligible to fill 2 identical positions in the computer science department"
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Senior Manager
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06 Jan 2008, 18:20
well , I could get the OA, but can someone please explain what is the significance of this statement
"If none of the candidates is eligible for a position in both departments",.
I thoght we were finding combinations of eligible candidates!
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06 Jan 2008, 18:41
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vscid wrote:
well , I could get the OA, but can someone please explain what is the significance of this statement
"If none of the candidates is eligible for a position in both departments",.
I thoght we were finding combinations of eligible candidates!

it means that the candidates of science department can not be eligible for the math department. Two groups are saperate, no overlap
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06 Jan 2008, 20:32
marcodonzelli wrote:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

7/1!*6! --> 7 * 10!/2!*8! --> 5*9 --> 5*9*7 =315

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07 Jan 2008, 15:54
sondenso wrote:
vscid wrote:
well , I could get the OA, but can someone please explain what is the significance of this statement
"If none of the candidates is eligible for a position in both departments",.
I thoght we were finding combinations of eligible candidates!

it means that the candidates of science department can not be eligible for the math department. Two groups are saperate, no overlap

got it!
had got confused with the wording.
thanks!
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Manager
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27 Sep 2009, 10:51
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

Ans: 315

7C1 * 10C2

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Manager
Joined: 17 Aug 2009
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09 Dec 2009, 09:20
This can be a tricky question in terms of wording. As we have to find out the different sets of both, we need to multiply each of the combinations.

Therefore 7C1 * 10C2 = 315

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24 Apr 2010, 14:09
is it for real 700-Level Question????

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02 Oct 2012, 01:18
GMATBLACKBELT wrote:
marcodonzelli wrote:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

7/1!*6! --> 7 * 10!/2!*8! --> 5*9 --> 5*9*7 =315

-----------------------------------------------------------------------
Can you please explain why is it 7C1 ?

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Math Expert
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02 Oct 2012, 01:30
1
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Expert's post
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Weirdo2989 wrote:
GMATBLACKBELT wrote:
marcodonzelli wrote:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

7/1!*6! --> 7 * 10!/2!*8! --> 5*9 --> 5*9*7 =315

-----------------------------------------------------------------------
Can you please explain why is it 7C1 ?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

As "none of the candidates is eligible for a position in both departments" then we have 7+10=17 candidates.

$$C^1_7*C^2_{10}=7*45=315$$: $$C^1_7$$ - choosing 1 from 7 and $$C^2_{10}$$ choosing 2 from 10 when order doesn't matter as 2 positions in computer science department are identical (XY is the same as YX).

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-university-will-select-1-of-7-candidates-eligible-103273.html
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Kudos [?]: 124064 [1], given: 12070

Re: prob prob   [#permalink] 02 Oct 2012, 01:30
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