Seven different lecturers are to deliver lectures in seven perday. A, B and C are three oftne lectures. The number of ways in which a routine for theday canr be made such that A delivers his lecture before B and B before C, is

Options

A. 420
B. 120
C. 210
D. none of these

Explanation

Let us consider the arrangements of 7 objects out of which three are identical and remaining distinct. In each arrangement of these 7 objects, let us mark the first identical item as P, second as Q and third as R. We find that in all the `(7!)/(3!)` arrangements P will occur prior to Q and Q will occur prior to R.
In the given sum also the required number of ways `=(7!)/(3!)=840`