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
In a football championship, there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is
Value of $r$ for which $^{15}{C_{r + 3}} = {\,^{15}}{C_{2r - 6}}$ is
If $^{{n^2} - n}{C_2}{ = ^{{n^2} - n}}{C_{10}}$, then $n = $
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
If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation