# Spaghetti Strands

**Discrete Mathematics**Level 5

The Tramp and the Lady are down to 5 strands of spaghetti (total of 10 ends) in their bowl. They decide to pick up a random end, and tie it to another randomly selected end. They will continue to do so until no ends remain, leaving them with just loops of spaghetti. The expected number of loops in the bowl has the form \(\frac {a}{b}\), where \(a\) and \(b\) are positive, coprime integers. What is the value of \(a+b\)?