JEE Advance - Mathematics (2020 - Paper 2 Offline - No. 14)
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 ..........
Answer
1080
Explanation
The groups of persons can be made only in 2, 2, 1, 1
$$ \therefore $$ 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
= $$\eqalign{ & {{6!} \over {{{(2!)}^2}{{(1!)}^2}(2!)(2!)}}(4!) \cr & = 360 \times 3 = 1080 \cr} $$
$$ \therefore $$ 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
= $$\eqalign{ & {{6!} \over {{{(2!)}^2}{{(1!)}^2}(2!)(2!)}}(4!) \cr & = 360 \times 3 = 1080 \cr} $$
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