$^n{P_r} \div ^n{C_r} = $

$3$ boys $B_i, i = 1, 2, 3$ and $6$ girls $G_i, i = 1, 2, . . . , 6$ are to be seated in a row. The number of ways they can be seated so that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

In an examination,the maximum marks for each of three subjects is $n$ and that for the fourth subject is $2n$. The number of ways in which a candidate can get $3n$ marks is

Let $A = \{(a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22\}$. Then $n(A)$ is equal to:

The total number of $3$-digit numbers,whose greatest common divisor with $36$ is $2$,is

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is