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# How many different ways to pick 3 letters from ABCDEFG, when

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Senior Manager
Joined: 01 May 2004
Posts: 335
Location: USA
How many different ways to pick 3 letters from ABCDEFG, when [#permalink]

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27 Nov 2004, 17:59
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How many different ways to pick 3 letters from ABCDEFG, when AB can't be together?
Manager
Joined: 30 Jul 2004
Posts: 101

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27 Nov 2004, 21:57
To choose 3 letters out of ABCDEFG without AB together :
we have to consider AB as ONE letter

so we have to choose 3 letters out of 6(since AB are one letter)

No. of ways to choosing are c(6,3) = 20.

Manager
Joined: 13 Oct 2004
Posts: 236

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28 Nov 2004, 10:47
There are 3 ways in which AB cant be together.

A Not B or B not A or Neither A Nor B
A Not B = 3(1. 5.4) = 60
B Not A = 3(1.5.4) = 60
Neither A Nor B = 5.4.3 = 60

180, if order matters.

If order doesnt matter: 5c2+5c2+5c3 = 30.

Last edited by prep_gmat on 28 Nov 2004, 18:25, edited 1 time in total.
Director
Joined: 31 Aug 2004
Posts: 606

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28 Nov 2004, 15:06
Various ways : 7C3

AB together : 5!

So 7C3-5!
Manager
Joined: 13 Oct 2004
Posts: 236

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28 Nov 2004, 18:27
Twixt,
7c3 - 5! would yield a negative number?.
Director
Joined: 16 Jun 2004
Posts: 891

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28 Nov 2004, 20:16
oops late on this one..

2C1*5C2 + 5C3 = 30.

2C1 because - either of A or B.
5C2 2 of the remaining 5 letters

5C3 - pick all three letters from the 5.
Director
Joined: 31 Aug 2004
Posts: 606

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29 Nov 2004, 03:57
I am sorry my answer was 7C3 - 5 and not 7C3 - 5! (5! makes no sense since there is only one slot left with 5 letters to put into...)

=5.6.7/6-5=35-5=30
Director
Joined: 07 Nov 2004
Posts: 683

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29 Nov 2004, 05:45
In a question like this do we assume that the order of the letters do not matter?
Manager
Joined: 31 Aug 2004
Posts: 162

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29 Nov 2004, 11:15
To Twist & Vprabhala,

Write out all the possibilities like the attached file?
Is there any better way to find this number?

Attachments

letters.doc [19 KiB]

Director
Joined: 31 Aug 2004
Posts: 606

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29 Nov 2004, 13:38
As order does not matter, you have to consider a 3 slots box. A is in 1st slot, B in the 2nd one, then you can put any of the 5 remaining letters in the last one.
Director
Joined: 07 Nov 2004
Posts: 683

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29 Nov 2004, 16:38
twixt wrote:
As order does not matter, you have to consider a 3 slots box. A is in 1st slot, B in the 2nd one, then you can put any of the 5 remaining letters in the last one.

Why is it assumed that order does not matter?
Director
Joined: 21 Sep 2004
Posts: 607

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30 Nov 2004, 10:31
as it is not mentioned.. we choose the lesser evil
30 Nov 2004, 10:31
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