To furnish a room in a model home, an interior decorator is to select 2 chairs and 12 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 of tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 Please help me with this problem. I'm usually confused with combination problems :s

dtl wrote:To furnish a room in a model home, an interior decorator is to select 2 chairs and 12 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 of tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 Please help me with this problem. I'm usually confused with combination problems :s Say the number of tables = n Now total number of possible combination = (Number of ways to select 2 chairs out of 5)*(Number of ways to select 2 tables out of n) = (5C2)*(nC2) = 10*(nC2) Now, 10*(nC2) = 150 => (nC2) = 15 => n(n - 1)/2 = 15 => n(n - 1) = 30 Now we can solve this quadratic n or we can go for a tricky shortcut. Note that only possible way to express 30 as a product of two consecutive integer is 5*6. Hence n must be equal to 6. The correct answer is A.

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