A stereo store is offering a special price on a complete set

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, Tcac, Technics A switch board 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 arc 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?

Solution

a) one component of each type is selected

4c1 *4c1*4c1*4c1 ( choosing 1 each from each type and then multiplying by product rule)

b)both reciever and cd are of Sony

only one choice for two type of selection hence

1*4c1*1*4c1

c)_none is to be sony

if all are sony then number of ways is = 1

if none is sony then total ways of choosing - all are sony = 4c1 *4c1*4c1*4c1 -1

d_at least one Sony is to be included:

one sony and rest three are others + two sony and rest two are others + three sony one other +allsony

= 1*4c1*4c1*4c1 +2*4c1*4c1+1*4c1 +1