Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

There are $5$ gentlemen and $4$ ladies to dine at a round table. In how many ways can they seat themselves so that no $2$ ladies are together?

In how many ways can $15$ members of a council sit along a circular table,if the Secretary must sit on one side of the Chairman and the Deputy Secretary on the other side?

Three horses $H_{1}, H_{2}, H_{3}$ entered a field which has $7$ portions marked $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}$ and $P_{7}$. If no $2$ horses are allowed to enter the same portion of the field,in how many ways can the horses graze the grass of the field?

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

There are $5$ apples,$4$ mangoes,$3$ oranges,and $1$ each of $2$ other varieties of fruits. The number of ways of selecting at least one fruit of each kind is