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?

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 3 times, and the number 3 is repeated twice.

The number of different time-tables is given by $\mathrm{p}(2,3,2)=\frac{7!}{2!3!2!}=210$