CAN someone help here? PLEASE....!

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svbla: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri May 15, 2009 1:35 am

by svbla » Sat Mar 19, 2016 2:06 pm

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?

I know it may be very simply for you, but it kills me!!!
I can figure it out that using combination formula to solve this issue, but why subtract 1 in the end? why? I don't get it!
What if it says at least 2of the wires for cable? what to do then?

I hate math so much, please help here if you could!!!

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Source: Beat The GMAT — Quantitative Reasoning | Sat Mar 19, 2016 2:06 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Mar 19, 2016 3:21 pm

Case 1: 2 Cable Wires Used

C1 C2 T1

C1 C2 T2

C1 C2 T3

2C2 x 3C1 = 1 x 3 = 3

Case 2: 1 Cable Wire Used

C1 T1 T2

C1 T1 T3

C1 T2 T3

C2 T1 T2

C2 T1 T3

C2 T2 T3

2C1 x 3C2 = 2 x 3 = 6

Total Number Of Combinations: 3 + 6 = 9

Marty Murray
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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Mar 19, 2016 4:10 pm

Hi svlba,

IF you were allowed to use any 3 wires (from the group of 5), then you could use the Combination Formula without having to do anything else:

Combinations = N! / K!(N-K)! = 5! / 3!2! = (5)(4) / (2)(1) = 10 possible combinations of 3 wires

HOWEVER, the prompt tells us that AT LEAST one cable wire must be included in the group of 3. There is ONE option that has 0 cable wires though (the one with all 3 telephone wires), so we have to subtract that one option from the total.

10 - 1 = 9

The number of possible combinations of wires is relatively small, so you could also have 'brute forced' this prompt - and just list out all of the options (as Marty pointed out).

GMAT assassins aren't born, they're made,
Rich

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Apr 15, 2016 1:50 pm

We've got two possibilities:

1: We only use one cable TV wire;
2: We use BOTH cable TV wires.

In the first case, we'd have (2 choose 1) * (3 choose 2), or 6. In the second, we'd have (2 choose 2) * (3 choose 1), or 3. So our total is 6 + 3, or 9.

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