A test consists of $6$ multiple choice questions, each having $4$ alternative ans wers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is
$135$
$140$
$125$
$130$
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
In a conference of $8$ persons, if each person shake hand with the other one only, then the total number of shake hands shall be
The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is
If $^n{C_{12}} = {\,^n}{C_6}$, then $^n{C_2} = $
The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to