$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

In a shop,there are $5$ types of ice-creams available. $A$ child buys $6$ ice-creams.
Statement-$1$: The number of different ways the child can buy the $6$ ice-creams is $^{10}C_5$.
Statement-$2$: The number of different ways the child can buy the $6$ ice-creams is equal to the number of different ways of arranging $6$ $A$'s and $4$ $B$'s in a row.

$A$ committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is: