Question

A train time-table must be compiled for various days of the week so that two trains a day depart for three days , one train a day for two days and three trains a day for two days . How many different time-tables can be compiled ?

• A. 140
• B. 210
• C. 133
• D. 72

Answer 1

Answer: (B)

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 equal to :
$p(2,3,2)=\frac{7!}{2!3!2!}=210$