# 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? - Mathematics

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

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 15 | Page 15