From among the 36 teachers in a college, one principal, one vice-principal and the teacher-in-charge are to be appointed. In how many ways can this be done?
Given: A total of three positions are to be given.
Number of ways to select principal is 36C1
Number of ways to select vice-principal is 35C1 (35 since one position is already given)
Number of ways to select teacher in charge is 34C1 (34 since two positions are already given)
Hence, total number of ways is 36C1 × 35C1 × 34C1 = 36 × 35 × 34 = 42840