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Permutations and combinations

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7 students of a hostel are to be allotted 7 beds. Among them Praveen does not want a bed next to Nandu because Nandu snores. Then in how many ways can you allot the beds?

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Best answer

7 students of hostle 7 beds

Praveen doesnt want a bed near Nandu

Total possible allotments

= 7!

= 720 × 7

= 5040

Cases when Nandu are together

= 6! × 2! 

= 720 × 2

= 1440

Allotment such that Praveen and Nandu are not together

= 5040 − 1440

= 3600

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