# Bibi's Malfunctioning Phone

**Discrete Mathematics**Level 4

Bibi wants to send invitations to some of her friends to come to her birthday party. She has contact information for 37 friends stored on her phone, but she only wants to invite 21 of those people to her party. She tries to send out a message to the 21 people, but her phone malfunctions and sends the message to three random contacts (uniformly chosen). The probability that exactly one person who got the invitation was not supposed to be invited to the party can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are positive, coprime numbers. What is the value of \(a+b\)?