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 (receive compact disc player, speakers, turntable). A purchase is offered a choice of manufacturer r 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: In how many ways can one component of each type be selected? 128 ways In how many ways can components be selected if both the receiver and the compact disc player are to be Sony? 16 ways In how many ways can components be selected if none is to be Sony? 54 Ways In how many ways can a selection be made if at least one Sony component is to be included ? 74 Ways 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? () at least one Sony component exactly one Sony component

Explanation / Answer

a)no of ways to select component of each type = 4*4*2*4 = 128

b)no of ways to select if both receiver and compact disc are to be sony = 1*1*2*4 = 8

c)no of ways to select if none of them are sony = 3*3*2*3 = 54

d)no of ways to select if at least component should be sony = 128-54 = 74

e)P(atleast one sony component) = 74/128 = 0.578125

P(exactly one sony component ) = (1*3*2*3+3*1*2*3+3*3*2*1)/128 = 54/128 = 0.421875

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