A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D?
Choices
A) 2/27	B) 4/27	C) 5/27	D) 8/27	E) 15/27
there are 6 distinct categories..   Since each category has to have at least 2 products..   let A have 2 and each thereafter has ONE more than previous..   so A,B,C,D,E, and F will have minimum 2+3+4+5+6+7 = 7*8/2 -1 = 28-1 =27..   therefore ONLY possibility of products in each due to restriction of TOTAL as 27 is 2,3,4,5,6,7 so D will have 5 products..   Probability = 5/27   ANSWER:5/27
<result>C</result>
A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If at-least 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D?