JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Permutations and Combinations

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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

Solution

The only split of six people among four rooms holding one or two each is

(2, 2, 1, 1)

. Choose which two of the four rooms hold two people in

(2 4) = 6

ways; then fill them by taking

2

of the

6

people for the first,

2

of the remaining

4

for the second, and one each for the two single rooms:

(2 6) (2 4) (1 2) (1 1) = 15 \times 6 \times 2 \times 1 = 180

. The total is

6 \times 180 = 1080

JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Numerical answer

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