danjuma wrote:To furnish a room 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 in the warehouse?
6
8
10
15
30
Number of ways to combine 2 chairs from 5 choices = 5C2 = 10.
Number of ways to combine 2 tables = (total ways to combine 2 chairs and 2 tables)/(number of ways to combine 2 chairs) = 150/10 = 15.
Now we can plug in the answer choices -- which represent the number of tables -- to see which answer choice yields 15 ways to choose 2 tables.
Answer choice C:
10C2 = 45. Eliminate C.
Need a smaller answer choice. Eliminate D and E.
Answer choice B:
8C2 = 28. Eliminate B.
The correct answer is A.
Answer choice A:
6C2 = 15. Success!
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