Those of you familiar with combinatorics should know that this is another way  of computing the third Catalan number.
FTP, How many 6-letter words made of three X‘s and three Y‘s are there such that the word  always has at least as many X‘s as Y‘s. Those of you familiar with combinatorics should know that this is another way  of computing the third Catalan number. Another way to do this problem is to compute the total number of six-letter  words that you can make with three X‘s and three Y‘s. The word cannot start with a Y or end with an X, so divide that  answer by four.
FTP, How many 6-letter words made of three X‘s and three Y‘s are there such that the word  always has at least as many X‘s as Y‘s.
5