 the number of possible ways he could assign breeds to his N cows so that this property holds. There are several ways to define what it means for a string of parentheses to be &quot;balanced&quot;. Perhaps the simplest definition is that there must be the same total number of ('s and )'s, and for any prefix of the string, there must be at least as many ('s as )'s. For example, the following strings are all balanced: () (()) ()(()()) while these are not: )( ())( ((()))) </span></p></div></div></div></div><di