Question: 1. In a programming class of seven students, the instructor wants each student to modify the program from a previous assignment, but no student should work on his or her own program. In how many ways can the instructor assign programs to the students?
2. Prove that S(m, n), the number of ways to partition a set of m elements into n blocks, is equal to 1·n! times the number of onto functions from a set with m elements to a set with n elements.