Directions: Solve the following problems completely. Students will be chosen to join the science field trip. In how many ways can the students from a class with 40 students be chosen? Answer: 361,904. Each guest shakes hands with everyone else. If there are 30 guests in a gathering, how many handshakes will be done? A soloist is auditioning for a musical play. If she is required to sing any three of the 8 prepared songs, in how many ways can she make her choice? Answer: 7.