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. . . . . .
$494$
$495$
$496$
$497$
If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
A person wants to climb a $n-$ step staircase using one step or two steps. Let $C_n$ denotes the number of ways of climbing the $n-$ step staircase. Then $C_{18} + C_{19}$ equals
The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is
A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to
In how many ways can one select a cricket team of eleven from $17$ players in which only $5$ players can bowl if each cricket team of $11$ must include exactly $4$ bowlers?