Probabilities

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salma: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Nov 03, 2007 5:54 pm

Probabilities

by salma » Fri Jan 25, 2008 3:17 pm

To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a 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 in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

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Source: Beat The GMAT — Problem Solving | Fri Jan 25, 2008 3:17 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Probabilities

by Stuart@KaplanGMAT » Fri Jan 25, 2008 3:28 pm

salma wrote:To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a 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 in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

We're choosing 2 out of 5 chairs and 2 out of n tables. We know that the total number of possible choices is 150.

So, we have:

5C2 * nC2 = 150

5*4/2 * nC2 = 150

10 * nC2 = 150

nC2 = 15

The easiest thing to do at this point is to backsolve. We know that n is greater than 5 (since 5C2 was only 10), but it shouldn't be that much more - let's try n=6:

6C2 = 6!/2!4! = 6*5/2 = 30/2 = 15.. perfect! Choose (A).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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Anand08: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Jan 27, 2008 10:06 pm; Location: Sydney, Australia

Please elaborate on the concept

by Anand08 » Sun Jan 27, 2008 11:37 pm

Hi Stuart,

Could you please elaborate further on the concept behind this solution?

Thanks,
Anand

Forging a little success..each day!

Quote

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon Jan 28, 2008 12:47 am

To which concept are you referring - combinations?

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pathaniaus: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed May 06, 2009 8:57 am; Thanked: 2 times

by pathaniaus » Sun Jan 03, 2010 8:16 pm

stuart,

the question states, tables and chairs that are all different from each other. i thought that with all things distinguishable, we use permutations i.e. n!/(n-r)! and not combinations n!/r!(n-r)!

thank you.

Udai Pathania

Quote

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon Jan 04, 2010 12:31 am

pathaniaus wrote:stuart,

the question states, tables and chairs that are all different from each other. i thought that with all things distinguishable, we use permutations i.e. n!/(n-r)! and not combinations n!/r!(n-r)!

thank you.

Udai Pathania

No - we use permutations when we care about the order of selection and combinations when order is irrelevant.

In this question, we don't care about the order in which we select the different pieces of furniture, we just about which pieces we select.

If, for example, we were selecting 4 chairs out of 7 and then arranging those chairs in a straight line, we'd use the permutations formula; if we were just selecting 4 chairs out of 7, we'd use the combinations formula.

On some permutations questions, we also worry about whether the items are distinct. I don't think I've ever seen a GMAT combinations question on which we had to worry about duplicates.

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Tue Jan 05, 2010 6:21 am

salma wrote:To furnish a room is a model home, an interior decorator is to select 2 chairs and 2 tables from a 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 in the warehouse?
6
8
10
15
30

I selected 30 but 6 is the correct answer.

Plzzz help.

Thx

5C2 x TC2 =150
5.4/2 x T ( T-1)/2 =150

T(T-1) =30
T^2 -T -30 =0
(T-6) ( T+5) =0

T =6
Choose A.

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sam117: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Thu Feb 09, 2012 9:04 am

by sam117 » Fri May 18, 2012 7:24 am

Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Fri May 18, 2012 11:19 am

sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks

Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.

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sam117: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Thu Feb 09, 2012 9:04 am

by sam117 » Fri May 18, 2012 11:27 am

Stuart Kovinsky wrote:
sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks
Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.

Ok but shouldn't "2 chairs and 2 tables" come directly before "that"?

Quote

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Fri May 18, 2012 12:45 pm

*TANGENT ALERT*

No math here, if you're looking for math, move along!

There's no need to put it directly before that (in fact, I challenge you to rewrite the sentence to put that where you want without causing a modification error in the remainder of the sentence) - the verb makes it clear to what "that" refers.

sam117 wrote:
Stuart Kovinsky wrote:
sam117 wrote:Hi, I know that this is a quant question. But am I right in saying that "that" has no clear referent here? It seems that "that" refers to "warehouse" instead of "chairs and tables". I found the wording of this question very weird and this led me to skip it in gmatprep. Please answer. Thanks
Hi!

Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can't be the referent of that.
Ok but shouldn't "2 chairs and 2 tables" come directly before "that"?