The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is
$4060$
$3605$
$455$
None of these
Out of $10$ white, $9$ black and $7$ red balls, the number of ways in which selection of one or more balls can be made, is
If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is