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6.Permutation and Combination
medium
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. . . . . .
A
$494$
B
$495$
C
$496$
D
$497$
(IIT-2020)
Solution
Selection of $4$ days out of $15$ days such that no two of them are consecutive
$={ }^{15-4+1} C _4={ }^{12} C _4$
$=\frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2}=11 \times 5 \times 9=495$
Standard 11
Mathematics
