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a 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 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

Grade:12

2 Answers

Atharva Baste
37 Points
7 years ago
the no 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 repeats twice, the number 2  repeats thrice, and the number 3repeated twice.
The number of different time-tables is given by :7!/ 2!3!2!=210
Anjuvi
13 Points
4 years ago
For train 1 number of ways you can choose 3 days from 7 days = \binom{7}{3}
For train 2 number of ways you can choose 2 days from rematning 4 = \binom{4}{2}
For train 3 number of ways you can choose 2 days from reamining 2 days=\binom{2}{2}
 
Total ways =\binom{7}{3}\binom{4}{2}
\binom{2}{2}=210

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