A participant can choose to consider ( 1 ) Remains single . Number of people reduce to ( x - 1 ) ( 2 ) Pairs with one of the ( x - 1 ) others . For every pairing , number of peopl reduce to ( x - 2 ) .
else return numberOfWays ( $ x - 1 ) + ( $ x - 1 ) * numberOfWays ( $ x - 2 ) ; }