Question

A train timetable must be compiled for various days of the week so that two trains twice a day depart for three days, one train daily for two days, and three trains once a day for two days. How many different timetables can be compiled?

• A. $140$
• B. $210$
• C. $133$
• D. $72$

Answer 1

The correct option is B $210$

The number of trains a day (the digits $1,2,3$) are three groups of like elements from which a sample must be formed.

In the time-table for a week, the number $1$ is repeated twice, the number $2$ is repeated thrice, and the number $3$ is repeated twice.

The number of different time-tables is given by

$(2,3,3)=\frac{7!}{2!3!2!}=210$