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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Solution

We have to select $4$ days.
Not selected days $= 11$ days
Gaps $= 12$
$∴$ Required number of ways $=^{12} C_{4} = \frac{12 \times 11 \times 10 \times 9}{24} = 495$

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We have to select 4 days. Not selected days =11 days Gaps =12 ∴ Required number of ways =12C4=12×11×10×924=495

We have to select $4$ days.
Not selected days $= 11$ days
Gaps $= 12$
$∴$ Required number of ways $=^{12} C_{4} = \frac{12 \times 11 \times 10 \times 9}{24} = 495$