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
$10 !$
$\frac{{10\,!}}{{5\,!}}$
$\frac{{10\,!}}{{{{(5\,!)}^2}}}$
None of these
A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first five question. The number of choices available to him is
There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to
The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included