Catalan numbers are a sequence of natural numbers that occurs in many interesting counting problems like following.
1) Count the number of expressions containing n pairs of parentheses which are correctly matched. For n = 3, possible expressions are ((())), ()(()), ()()(), (())(), (()()).

2) Count the number of possible Binary Search Trees with n keys (See this)

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3. ranga ramasesh is the operations manager for a firm that is trying to decide which one of four countries it should research for possible outsourcing providers. the first step is to select a country based on cultural risk factors, which are critical to eventual business success with the provider. ranga has reviewed outsourcing provider directories and found that the four countries in the table that follows have an ample number of providers from which they can choose. to aid in the country selection step, he has enlisted the aid of a cultural expert, john wang, who has provided ratings of the various criteria in the table. the resulting ratings are on a 1 to 10 scale, where 1 is a low risk and 10 is a high risk. john has also determined six criteria weightins: trust, with a weight of 0.3; quality, with 0.2; religious, with 0.1; individualism, with 0.2; time, with 0.1; and uncertainity, with 0.1. using the factor-rating method, which country should ranga select? why? (2 points)

This isn't about school but every time it tells me to watch an ad to unlock the answer to a question it prompts a survey and it just keeps loading. so i haven't been able to get answers for my tests in like a week.