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  4. 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 ?

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Q. 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 ?

Permutations and Combinations

Solution:

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