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Suppose 5 students are staying in a hall in a hostel and they are allotted 5 beds. Among them, Paresh does not want a bed next to Anjum because Anjum snores. Then, in how many ways can you allot the beds?
Let the beds be numbered 1 to 5.
Suppose Anjum is allotted bed number 1. Then, Paresh cannot be allotted bed number 2.
So, Paresh can be allotted a bed in 3 ways. After allotting a bed to Paresh, the remaining 3 students can be allotted beds in 3! Ways. So, in this case the beds can be allotted in 3 × 3! = 18 ways.
Anjum is allotted bed number 5.
Then, Paresh cannot be allotted bed number 4. As in Case 1, the beds can be allotted in 18 ways.
Anjum is allotted one of the beds numbered 2, 3 or 4
Paresh cannot be allotted the beds on the right-hand side and left-hand side of Anjum's bed.
For example, if Anjum is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Paresh.
Therefore, Paresh can be allotted a bed in 2 ways in all these cases. After allotting a bed to Paresh, the other 3 can be allotted a bed in 3! Ways.
Therefore, in each of these cases, the beds can be allotted 2 × 3! = 12 ways.
=> The beds can be allotted in (2 × 18 + 3 × 12) =72 = 72 ways
By: Munesh Kumari ProfileResourcesReport error
Noorbir Singh 6 months ago
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