Problem Solving

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!

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

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!

Check:

You could also plug in the answer choices and check

6c2*5c2 will be 150

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