1) A multispeed bicycle has 4 sprockets in front and 6 sprockets on the rear wheel. The rider uses the bicycle's front and rear shift mechanism to move the chain from one front or rear sprocket to another.
a) how many speeds does the bicycle have?
b) is it correct to say that a speed requires a particular front and a particular rear sprocket, or that a speed requires a particular front or rear sprocket?
2) A committee is being developed that will consist of 1 freshmen and 1 sophomores. The classes have narrowed it down to 4 freshmen and 6 sophomores.
a) how many different ways can this committee be formed?
3) Compare your answers from questions 1a and 2. If they are different, describe why.