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combination problem

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by locke322 » Sun Oct 12, 2008 5:47 pm
Hello this is a question from the GMAT prep practice test #1.

To furnish a rom in 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?

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

The answer is 6. But can someone please explain why the answer is 6?

Thanks so much!
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by vishubn » Sun Oct 12, 2008 6:12 pm
Hi....

We know that there are 150 possible comb

and 2 chairs and 2 tables to be selected

5c2*nc2=150
nc2=15
solve for n and u get n=6

vishu
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by cramya » Sun Oct 12, 2008 7:03 pm
Let x be the number of tables

2 chairs can be selected from 5 in 5c2 ways

2 tables can from x tables in xc2 ways

We are given 5c2 * xc2 (total combinations of picking 2 chairs from 5 chairs and 2 tables fromm x tables; The reason you multiply is because there are different set of objects from which you choose r in each case)

= 150

i.e. 5c2 * xc2 = 150

5*4/2 * xc2 = 150

xc2 = 15

x(x-1) (x-2)! / (x-2)! 2! = 15

x(x-1) = 30
x^2-x-30 = 0

x=-5 x=6

x cant be negative so x=6 in this case

Hope this helps!
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by cramya » Sun Oct 12, 2008 7:06 pm
Check:

You could also plug in the answer choices and check

6c2*5c2 will be 150
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by cramya » Sun Oct 12, 2008 7:12 pm
Please take this as a request. Instead of including the answer right below the question use the spoiler function to hide it. This would enable other users to work on getting to the right solution without seeing the official answer

Refer to
https://www.beatthegmat.com/etiquette-fo ... 20629.html

Good luck!
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