A stereo store is offering a special price on a complete set of components (rece

Question

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:

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?
ways

(b) In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?
ways

(c) In how many ways can components be selected if none is to be Sony?
ways

(d) In how many ways can a selection be made if at least one Sony component is to be included?
ways

(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? (Round your answer to three decimal places.)

Receiver: Kenwood, Onkyo, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony, Technics Speakers: Boston, Infinity Turntable: Onkyo, Sony, Teac, Technics

Explanation / Answer

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:

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?
ways

4*4*2*4 = 128

(b) In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?
4*2*4 =32 ways

(c) In how many ways can components be selected if none is to be Sony?
128 - 32 = 96 ways

(d) In how many ways can a selection be made if at least one Sony component is to be included?
128 ways

Receiver: Kenwood, Onkyo, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony, Technics Speakers: Boston, Infinity Turntable: Onkyo, Sony, Teac, Technics

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