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Question

The number of ways in which the time table for Monday can be made if there must be 5 lessons to be taught that day (Algebra, Geometry, Calculus, Trigonometry, Vector) and topics Algebra and Geometry cannot immediately follow each other are

A
72
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B
5!
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C
3×5!2
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D
6!
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Solution

The correct option is A 72
×V×C×T×
On these 4 crosses we can arrange two subjects (Algebra and Geometry) in 4P2.
And V,C,T can be arranged in 3! ways.
Hence, total number of ways =4P2.3!=72

Alternate :
The number of required ways = Total ways without restriction Total ways when Algebra and Geometry are one after the other.
Total ways without restriction =5!
Total ways when Algebra and Geometry are one after the other =2!×4!
(Consider Algebra and Geometry as one object and interchange among themself)
The number of required ways =5!2!×4!=72

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