Question

Seven different lecturers are to deliver lectures in seven periods of a class on a particular day. $A,B$ and $C$ are three of the lecturers. The number of ways in which a routine for the day can be made such that $A$ delivers his lecture before $B$, and $B$ before $C$, is

• A. $420$
• B. $120$
• C. $210$
• D. $noneofthese$

Answer 1

Answer: (D)

$noneofthese$

As the order of A, B and C is not to be changed they can be treated as identical in arrangement
so number of ways $=\frac{7!}{3!}=\mathrm{7.6.5.4}=840$