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# To furnish a room in a model home an interior decorator is

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Director
Joined: 06 Feb 2006
Posts: 881
To furnish a room in a model home an interior decorator is  [#permalink]

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25 Feb 2006, 06:38
1
7
00:00

Difficulty:

25% (medium)

Question Stats:

79% (00:56) correct 21% (01:08) wrong based on 225 sessions

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To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?

A) 6
B) 8
C) 10
D) 15
E) 30

OPEN DISCUSSION OF THIS QUESTION IS HERE: to-furnish-a-room-in-a-model-home-an-interior-decorator-is-86144.html
Director
Joined: 06 Feb 2006
Posts: 881
Re: To furnish a room in a model home an interior decorator is  [#permalink]

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25 Feb 2006, 13:56
2
Ok...
This one is actually easy one...

Total number of ways to choose 2 chairs from 5= 5C2=10

Total number of combination=150

That means we need get 15 combinations from the selection of tables....

Screening through the answers.... 6C2=15..... 15*10=150

Does anybody have some kind of different approach?
CEO
Joined: 20 Nov 2005
Posts: 2840
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Re: To furnish a room in a model home an interior decorator is  [#permalink]

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25 Feb 2006, 19:15
5
4
My approach is almost like your's but little different

5C2 * nC2 = 150

10 * n(n-1)/2 = 150
n(n-1) = 30. So n = 6
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Math Expert
Joined: 02 Sep 2009
Posts: 47981
Re: To furnish a room in a model home an interior decorator is  [#permalink]

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24 Jul 2014, 14:54
2
2
To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?

A) 6
B) 8
C) 10
D) 15
E) 30

$$C^2_5*C^2_t=150$$, where $$t$$ is the # of tables --> $$C^2_5*C^2_t=150$$ --> $$C^2_t=15$$ --> $$\frac{t!}{2!(t-2)!}=15$$ --> $$(t-2)!$$ will cancel out --> $$(t-1)t=30$$ --> $$t=6$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: to-furnish-a-room-in-a-model-home-an-interior-decorator-is-86144.html
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Posts: 7755
Re: To furnish a room in a model home an interior decorator is  [#permalink]

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28 Jul 2018, 21:37
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Re: To furnish a room in a model home an interior decorator is &nbs [#permalink] 28 Jul 2018, 21:37
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