First slide

Combinations

Question

$An engineer is required to visit a factory for exactly four days during the first 15 days of every$
$month and it is mandatory that no two visits take place on consecutive days. Then the number of all$
$possible ways in which such visits to the factory can be made by the engineer during 1 - 15 June 2021 is$

Moderate

Solution

$Selection of 4 days out of 15 days such that no two of them are consecutive$
$\begin{array}{l} =^{15 - 4 + 1} C_{4} =^{12} C_{4} (n - r + 1_{C_{r}}) \\ = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2} = 11 \times 5 \times 9 = 495 \end{array}$

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