# From among the 36 teachers in a college, one principal,

Question:

From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?

Solution:

Total number of teachers in the college = 36

Number of ways of  selecting a principal = 36

Number of ways of selecting a vice-principal = 35 (as one of the teacher is already being selected for the post of principal)

Similarly, number of ways of selecting the teacher-incharge = 34

$\therefore$ Total number of ways of selecting all the three $=36 \times 35 \times 34=42840$