On the average $$100$$ customers arrive at a place each hour, and on the average the server can process $$120$$ customers per hour. What is the proportion of time the server is idle?

The manufacturing area of a plant is divided into four quadrants. Four machines have to located one in each quadrant. The total number of possible layouts is

Interference in a pair of gears is avoided, if the addendum circles of both the gears intersect common tangent to the base circles with in the points of tangency.