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# Of the 5 distinguishable wires that lead into an apartment,

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Intern
Joined: 16 Aug 2011
Posts: 8
GMAT Date: 10-15-2011

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20 Aug 2011, 22:15
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:44) correct 35% (02:02) wrong based on 178 sessions

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Of the 5 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

My Approach is as follows :
Since there are 2 cables wires and 3 TV wires ....and there has to be a minimum of 1 cable wire in the combination of three wires so we have 2 cases :

Case 1 - Choosing 1 cable wire out of 2 and choosing 2 TV wires out of 3 ...This is 2C1 * 3C2
OR
Case 2 - Choosing 1 cable wire wire in 1st place, then choosing 1 cable wire for 2nd place and finally choosing 1 TV wires out of 3 ...This is 1 * 1 * 3C1
Thus answer is case 1 OR Case 2

This is 2C1 * 3C2 + 1 *1 * 3C1 = 6 + 3 = 9 ...
Please correct me if I am wrong here.
Manager
Joined: 20 Aug 2011
Posts: 128
Re: Conbinations : Wires Problem  [#permalink]

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20 Aug 2011, 22:24
1
There is another approach
There are 5 wires in all
2 cable and 3 telephone service

To find the required combinations you can subtract the no. of combinations of all telephone wires from all possible combinations.

Required no. of combinations= 5C3-3C3=10-1=9

Hope this helps
Intern
Joined: 16 Aug 2011
Posts: 8
GMAT Date: 10-15-2011
Re: Conbinations : Wires Problem  [#permalink]

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20 Aug 2011, 23:28

Thanks..for this approach...
Manager
Joined: 18 Aug 2011
Posts: 50
Re: Conbinations : Wires Problem  [#permalink]

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20 Aug 2011, 23:42
C1 T1 T2
C1 T1 T3
C1 T2 T3

C2 T1 T2
C2 T1 T3
C2 T2 T3

C1 C2 T1
C1 C2 T2
C1 C2 T3
Manager
Joined: 20 Aug 2011
Posts: 128
Re: Conbinations : Wires Problem  [#permalink]

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20 Aug 2011, 23:43
Hi Anand,

You're welcome.
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Intern
Joined: 06 Apr 2011
Posts: 49
Location: India
Re: Conbinations : Wires Problem  [#permalink]

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21 Aug 2011, 07:34
There is another approach
There are 5 wires in all
2 cable and 3 telephone service

To find the required combinations you can subtract the no. of combinations of all telephone wires from all possible combinations.

Required no. of combinations= 5C3-3C3=10-1=9

Hope this helps

Thanks blink. this approach is easy to follow.
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Regards,
Asher

Director
Joined: 01 Feb 2011
Posts: 658
Re: Conbinations : Wires Problem  [#permalink]

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21 Aug 2011, 07:36
atleast one cable = total - no cable

= 5c3 - 3c3 = 9

Manager
Joined: 20 Aug 2011
Posts: 128
Re: Conbinations : Wires Problem  [#permalink]

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21 Aug 2011, 07:40
You're welcome asher
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Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Senior Manager
Joined: 23 Oct 2010
Posts: 350
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: Conbinations : Wires Problem  [#permalink]

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10 Mar 2013, 01:42
(5*4*3)/3! -(3*2*1)/3! =9
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Intern
Joined: 07 Mar 2013
Posts: 25
Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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29 Nov 2013, 02:34
Hi Bunuel,

Have solved this by using this method : 3C2 X 2C1 + 3C1 X 2C2 = 9.

Is this correct ?
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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29 Nov 2013, 02:43
2
vishalrastogi wrote:
Hi Bunuel,

Have solved this by using this method : 3C2 X 2C1 + 3C1 X 2C2 = 9.

Is this correct ?

Yes, it is. It's a direct approach in contrast to {total}-{restriction} approach used in the posts above.
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Intern
Joined: 07 Mar 2013
Posts: 25
Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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29 Nov 2013, 03:49
Bunuel wrote:
vishalrastogi wrote:
Hi Bunuel,

Have solved this by using this method : 3C2 X 2C1 + 3C1 X 2C2 = 9.

Is this correct ?

Yes, it is. It's a direct approach in contrast to {total}-{restriction} approach used in the posts above.

Thanks Bunuel. I always have my fingers crossed when I solve combinations.
Senior Manager
Joined: 08 Jun 2015
Posts: 432
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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14 Apr 2018, 08:28
+1 for option D. (2c1*3c2)+(2c2*3c1). The answer comes to 9.
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Re: Of the 5 distinguishable wires that lead into an apartment, &nbs [#permalink] 14 Apr 2018, 08:28
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