How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?

If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

There are 5 parallel lines on the plane. On the same plane, there are $n$ other lines that are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of $n$?

Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is _________.

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is _________.

Out of 13 objects, 4 are indistinguishable and the rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.