JEE Advanced 2020 Paper 2Question 1
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 ____
Permutation and Combination
Answer$495$
Solution
Choosing 4 non-consecutive days from 15: $\binom{15-4+1}{4}=\binom{12}4=495$.