How many balanced lists of n left and n right parentheses are there? 

A list of parentheses is said to be balanced if there are the same number of left parentheses as right, and as we count from left to right we always find at least as many left parentheses as right parentheses.
For example, (((()()))()) is balanced and ((()) and (()()))(() are not.

Question:How many balanced lists of n left and n right parentheses are there?

HINT: Find a bijection between lattice paths and lists of parentheses.

I know that my answer is going to be what is on the .PNG file, usless it it wrong. 
It is subtracting the total paths - bad paths
I am just unsure the steps to get to the answer.  

Discrete Mathematics Combinatorics
Lalo G Lalo G
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Matchmaticians  How many balanced lists of n left and n right parentheses are there?  File #1 File #1 (PNG)
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