In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be 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

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

If $110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear,then the value of $n$ is:

The number of $5$ digit telephone numbers having at least one of their digits repeated is

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.