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36 teachers are there.

need to appoint:  1 principal (P), 1 vice principal (VP), 1  teacher in charge (T).

principal in 36 ways.  any of teachers.
vice principal in 35 ways from any teacher excepting the principal.
teacher in charge in 34 ways,  any teacher excepting  principal and vice principal.

total number of ways:  36 * 35 * 34    =  ³⁶P₃

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