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Of the 5 distinguishable wires that lead into an apartment,

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

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New post 20 Aug 2011, 23:15
1
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:20) correct 35% (01:36) wrong based on 174 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. :)
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Re: Conbinations : Wires Problem  [#permalink]

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New post 20 Aug 2011, 23:24
1
Your approach is correct.
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
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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 00:28
Grt blink005

Thanks..for this approach...
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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 00:42
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
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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 00:43
Hi Anand,

You're welcome.
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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 08:34
blink005 wrote:
Your approach is correct.
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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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 08:36
atleast one cable = total - no cable

= 5c3 - 3c3 = 9

Answer is D.
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Re: Conbinations : Wires Problem  [#permalink]

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New post 21 Aug 2011, 08:40
You're welcome asher
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Re: Conbinations : Wires Problem  [#permalink]

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New post 10 Mar 2013, 02:42
(5*4*3)/3! -(3*2*1)/3! =9
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Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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New post 29 Nov 2013, 03:34
Hi Bunuel,

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

Is this correct ?
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Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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New post 29 Nov 2013, 03:43
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Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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New post 29 Nov 2013, 04:49
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.
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Re: Of the 5 distinguishable wires that lead into an apartment,  [#permalink]

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New post 14 Apr 2018, 09:28
+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, 09:28
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