In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point $P$ and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?

Note: The figure shown is representative.

A fair six-faced dice, with the faces labelled ' 1 ', ' 2 ', ' 3 ', ' 4 ', ' 5 ', and ' 6 ', is rolled thrice. What is the probability of rolling ' 6 ' exactly once?

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of