JEE Advanced 2020 · Paper 2 · Mathematics Q13

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MathematicsNumerical+4Question 49 of 54

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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Answer and worked solution

Official answer: 495

Gap counting. Choosing 4 non-consecutive days out of 15 is the same as placing 4 visits among 11 non-visit days with at most one visit in each of the 12 gaps:
$\binom{15-4+1}4=\binom{12}4=495.$
Answer: 495

Topics:Combinations

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JEE Advanced 2020 · Paper 2, Mathematics question 13