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

Question

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  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

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

We need to put 4 stick (identical) between 11 balls (identical) such that no 2 stick are together 12C4​=495

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