In how many different ways can the letters of the word $ALLAHABAD$ be permuted?

The total number of numbers greater than $100$ and divisible by $5$,that can be formed from the digits $3, 4, 5, 6$,if no digit is repeated is:

The number of triangles that can be formed by $5$ points on a line and $3$ points on a parallel line is

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

$3$ boys and $3$ girls are to be seated around a circular table. Among the boys,$X$ does not want any girl as a neighbour,and among the girls,$Y$ does not want any boy as a neighbour. How many such arrangements are possible?

Let $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is: