In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together
$1540$
$1450$
$1504$
$1405$
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
How many numbers of $6$ digits can be formed from the digits of the number $112233$
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together
The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is $...........$.