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The set S has 36 different subsets each of which contains

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The set S has 36 different subsets each of which contains [#permalink]

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New post 17 Aug 2014, 23:44
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The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly three elements each?

A. 24
B. 42
C. 54
D. 72
E. 84
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Aug 2014, 03:57, edited 2 times in total.
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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 18 Aug 2014, 02:02
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nC2 = 36
=> n*(n-1)/2 = 36

=> n = 9

nC3 = 9C3 = 84

So, Answer is E.

Hope it helps!
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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 02:29
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nC2 = 36
=> n*(n-1)/2 = 36

Explain this portion please.

nktdotgupta wrote:
nC2 = 36
=> n*(n-1)/2 = 36

=> n = 9

nC3 = 9C3 = 84

So, Answer is E.

Hope it helps!

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Arindam Sur
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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 02:34
n*(n-1) = 36*2 = 72
There are two ways of solving this
Method1:
n*(n-1)=72 = 9*8
n*(n-1) = 9*(9-1)
=> n =9

or n*(n-1) = -9 * -8
=> n*(n-1) = (-8)*(-8-1)
=> n = -8
n cant be negative so, n = 9

Method 2:
n*(n-1) = 72
=> n^2 - n - 72 =0
=> n^2 -9n + 8n - 72 = 0
=> (n-9)*(n+8) = 0
=> n= -8, 9
n cant be negative, so n =9

hope it helps!
arindamsur wrote:
nC2 = 36
=> n*(n-1)/2 = 36

Explain this portion please.

nktdotgupta wrote:
nC2 = 36
=> n*(n-1)/2 = 36

=> n = 9

nC3 = 9C3 = 84

So, Answer is E.

Hope it helps!

_________________

Ankit

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Kudos [?]: 793 [0], given: 59

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WE: Research (Education)
Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 02:37
I dont understand how do you derived n*(n-1)/2 from nC2
=>

nktdotgupta wrote:
n*(n-1) = 36*2 = 72
There are two ways of solving this
Method1:
n*(n-1)=72 = 9*8
n*(n-1) = 9*(9-1)
=> n =9

or n*(n-1) = -9 * -8
=> n*(n-1) = (-8)*(-8-1)
=> n = -8
n cant be negative so, n = 9

Method 2:
n*(n-1) = 72
=> n^2 - n - 72 =0
=> n^2 -9n + 8n - 72 = 0
=> (n-9)*(n+8) = 0
=> n= -8, 9
n cant be negative, so n =9

hope it helps!
arindamsur wrote:
nC2 = 36
=> n*(n-1)/2 = 36

Explain this portion please.

nktdotgupta wrote:
nC2 = 36
=> n*(n-1)/2 = 36

=> n = 9

nC3 = 9C3 = 84

So, Answer is E.

Hope it helps!

_________________

If you like my post give me kudos.

Arindam Sur
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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 13:28
Why nc2 = 36 ?

What I understand from question is that s = ((a1,b1),(a2,b2),(a3,b3),(a4,b4)...............(a36,b36))

Is this wrong understanding of question ? Kindly help

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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 13:38
The Set S has "n" elements {x1,x1,...,xn}

Out of these "n" elements if we try to make subset of two element each then we can make 36 such subsets, which are correctly denoted by you as (a1,b1),(a2,b2),(a3,b3),(a4,b4)...............(a36,b36)
So, S' = (a1,b1),(a2,b2),(a3,b3),(a4,b4)...............(a36,b36)
(Note a ' after S in previous line)

Now, to find out the number of elements in the set S we are given by we can make 36 subsets of two elements each,
So number of subsets of two element each which can be formed from a Set S which has n elements = nC2

read the second half of the question which says "How many subsets of S could contain exactly three elements each"
So, S is the set of "n" elements and not the Set of subsets of two elements

Hope it helps!

paandey wrote:
Why nc2 = 36 ?

What I understand from question is that s = ((a1,b1),(a2,b2),(a3,b3),(a4,b4)...............(a36,b36))

Is this wrong understanding of question ? Kindly help

_________________

Ankit

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How to Solve :
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The set S has 36 different subsets each of which contains [#permalink]

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New post 21 Aug 2014, 22:58
It was problematic for me to realize that n!/(n-2)!=n(n-1)

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Re: The set S has 36 different subsets each of which contains [#permalink]

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New post 15 Oct 2017, 04:27
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Re: The set S has 36 different subsets each of which contains   [#permalink] 15 Oct 2017, 04:27
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