The number of arrangements of the letters of the word $SALOON$,if the two $O$'s do not come together,is

If the letters of the word "$CAPITAL$" are permuted in all possible ways and the words are arranged in a dictionary order,then the rank of the word "$CAPITAL$" is

There are $11$ distinct books on a shelf,consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. In how many ways can they be arranged such that books of the same subject are always kept together?

The number of ways to seat $3$ men and $2$ women in a bus such that the total number of seated men and women on each side is $3$ is:

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many $3$-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

The number of ways of arranging the letters of the word $BANANA$ so that the two $N$s do not come together is: