$7$ 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?

3600

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2400

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2440

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3680

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Solution

The correct option is A $3600$
$7$ students of hostle $7$ beds
Praveen doesnt want a bed near Nandu
Total possible allotments
$= 7! = 720 \times 7 = 5040$
Cases when Nandu are together
$= 6! \times 2! = 720 \times 2 = 1440$
Allotement such that praveen and Nandu are not together
$= 5040 - 1440 = 3600$

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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?

The correct option is A 36007 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=1440Allotement such that praveen and Nandu are not together =5040−1440=3600

$7$ 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?