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Grade 12Algebra

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

Bharadwaj Varma

9 Years agoGrade 12

2 Answers

Atharva Baste

9 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

7 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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