Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is
$\frac{{10\;!}}{6}$
$3\;!\;7\;!$
$^{10}{P_3}\;.\;7\;!$
None of these
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
The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
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
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is