A stereo store is offering a special price on a complete set
of components (receiver, compact disc player, speakers,
turntable). A purchaser is offered a choice of manufacturer
for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to
hook together any selection of components (consisting of
one of each type). Use the product rules to answer the
following questions:
a. In how many ways can one component of each type be
selected?
b. In how many ways can components be selected if both
the receiver and the compact disc player are to be Sony?
c. In how many ways can components be selected if none is
to be Sony?
d. In how many ways can a selection be made if at least one
Sony component is to be included?
e. If someone flips switches on the selection in a completely
random fashion, what is the probability that the
system selected contains at least one Sony component?
Exactly one Sony component?