A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:Receiver: Kenwood, Onkyo, Pioneer, Sony, SherwoodCD Player: Onkyo, Pioneer, Sony, TechnicsSpeakers: Boston, Infinity, PolkCassette Deck: Onkyo,
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD Player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
A switch board display in the store allows a customer to hooktogether any selection of components (consisting of one of eachtype). Use the product rules to answer the followingquestions.
a. In how many ways can one component of each type beselected?
b. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
c. In how many ways can components be selected if noneis to be sony?
d. In how many ways can a selection be made if at leastone sony component is to be included?
e. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component? Exactly onesony component?