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 p

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_____

TestHub · Accepted Answer

Selection of 4 non-consecutive days out of 15 days is same as first remove 4 objects from 15 objects, so remainging objects are 11 having 12 gaps in which these 4 objects can be placed again. So, total number of ways is C 4 12 = 12 . 11 . 10 . 9 4 . 3 . 2 . 1 = 495 .

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