Roger is renting a tuxedo for prom. once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes. how many different ways can he select his attire for the prom?

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?