2. (Sec. 2.3) An electronics store is offering a special price on a complete set
ID: 3353036 • Letter: 2
Question
2. (Sec. 2.3) An electronics 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: Oknya, 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) (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?Explanation / Answer
a)One component of each type can be selected in 5*4*3*4=240 ways
b)If both receiver and compact disk player is fixed as Sony then the number of ways left are 3*4=12
c)If none is to be Sony then the number of ways are 4*3*3*3=108
d)If atleast one Sony component is to be included then we use the complement as Total ways -Ways in which no Sony component is selected thus 240-108=132
e)Probability of atleast one sony component=132/240 and for exactly one Sony component =(27+36+36)/240=99/240
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