Answer these questions independently of each other.

In the different arrangements of the word RAINBOW, how many words are there in which $\mathrm{A}$ is always before / and / is always before $\mathrm{O} ?$

In the different arrangements of the word RAINBOW, how many words are there in which vowels are always before the consonants?

Answer these questions independently of each other.

In the different arrangements of the word RAINBOW. how many words are there in which vowels occupy odd positions?

Answer these questions independently of each other.

$5$ men and $4$ women are to be seated for a dinner, in a row, such that no two persons of the same sex sit together. Find the number of ways in which this arrangement can be done.

Answer these questions independently of each other.

$5$ men and $4$ women are to be seated for a dinner, in a row, such that no two men sit together. Find the number of ways in which this arrangement can be done.

Answer these questions independently of each other.

$5$ men and $4$ women are to be seated for a dinner, in a row, such that no two women sit together. Find the number of ways in which this arrangement can be done.

Answer these questions independently of each other.

$5$ men and $4$ women are to be seated for a dinner, in a row, such that women occupy the even places. Find the number of ways in which this arrangement can he done

Answer these questions independently of each other.

$6$ men and $3$ women are to be seated for a dinner, in a row, such that no two women sit together. Find the number of ways in which this arrangement can be done.

Answer these questions independently of each other.

$4$ men and $4$ women are to be seated for a dinner, in a row, such that men and women sit alternately. Find the number of ways in which this arrangement can be done.