In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together
$1540$
$1450$
$1504$
$1405$
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
Statement$-1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3 .$
Statement$-2:$ The number of ways of choosing any $3$ places from $9$ different places is $^9C_3 $.
All possible two factors products are formed from numbers $1, 2, 3, 4, ...., 200$. The number of factors out of the total obtained which are multiples of $5$ is
Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.
In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?