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Number of ways in which 32 identical blankets can be distributed among 4 persons so that each of them gets number of blankets which are divisible by 2 but not by 4 is $^{K} C_{3}$
Then K=______

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answer is 9.

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Detailed Solution

Each one should get $4 λ + 2$ blankets where $λ \in W$
$∴ (4 λ_{1} + 2) + (4 λ_{2} + 2) + (4 λ_{3} + 2) + (4 λ_{4} + 2) = 32 \to λ_{1} + λ_{2} + λ_{3} + λ_{4} = 6.$ Number of ways $^{6 + 4 - 1} C_{4 - 1} =^{9} C_{3}$

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