Question

Seven different lecturers are to deliver in seven periods of a class on a particular day $A,B$ and $C$ are three of the lectures. 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. $210$
• B. $420$
• C. $840$
• D. $noneofthese$

Answer 1

The correct option is C $840$

We need to reserve 3 slots for A, B, C

There are $\frac{\mathrm{7.6.5}}{3.2}=35$ sets

of 3 schedule slots that we can reserve for A,B,C

The remaining $7-3=4$ slots will be filled by other lecturers in any order.

There are $4!=24$ possible permutations for rest 4 lecturers.

Combining those choices there are $35\times 24=840$

schedules for 7 lecturers.