Counting Candy Sequences: An Enumeration Problem

[摘要] A bottle contains 7 Type A and 7 Type B candies. Each morn­ing, you select two candies at random: If they are of opposite types, eat them both; otherwise, eat one and return the other to the bottle. Continue until all candies are eaten. If ever the bottle contains only one candy, select and eat it. How many distinct candy sequences are possible?.

[学科分类] 社会科学、人文和艺术（综合）

[关键词] Recursive relation;paths on a graph;Delannoy numbers;inner product;mathematical induction.