How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

The number of ways in which a committee of $6$ members can be formed from $8 $ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

A committee of $4$ persons is to be formed from $2$ ladies, $2$ old men and $4$ young men such that it includes at least $1$ lady, at least $1$ old man and at most $2$ young men. Then the total number of ways in which this committee can be formed is

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

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