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QJEEAdv20Ma8dc9: JEE Advanced 2020 Mathematics - Class 11 JEEAdv20Ma8dc9 Solution: In a hotel, four rooms are available. Six persons are to be…

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is ..........

Step-by-Step Verified Solution

The groups of persons can be made only in 2, 2, 1, 1

∴ So the number of required ways is equal to number of ways to distribute the 6 distinct objects in group sizes 1, 1, 2 and 2

= 6!(2!)2(1!)2(2!)(2!)(4!)=360×3=1080

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