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. . . . . .
$494$
$495$
$496$
$497$
Let $S=\{1,2,3,5,7,10,11\}$. The number of nonempty subsets of $S$ that have the sum of all elements a multiple of $3$ , is $........$
If $\sum\limits_{i = 0}^4 {^{4 + 1}} {C_i} + \sum\limits_{j = 6}^9 {^{3 + j}} {C_j} = {\,^x}{C_y}$ ($x$ is prime number), then which one of the following is incorrect
Determine $n$ if
$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is