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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
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B
210
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C
133
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D
72
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Solution

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)=7!2!3!2!=210

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