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  4. An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during 1-15 June 2021 is

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Q. An engineer is required to visit a factory for exactly four days during the first $15$ days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is _____

JEE AdvancedJEE Advanced 2020

Solution:

We need to put $4$ stick (identical) between $11$ balls (identical) such that no $2$ stick are together
${ }^{12} C _{4}=495$