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 96 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.) at least one Sony component exactly one Sony component

Explanation / Answer

a.

In how ways can 1 component of each type be selected?

3 Receiver* 4 CDP * 2 Speakers* 4 TT

=3*4*2*4

=96 ways

b.

If both compact disc and receiver are of Sony then:

1 Receiver type * 1 CDP * 2 Speakers * 4 TT

= 8

c.

If none is of sony then:

2 Receivers * 3 CDP*2 Speakers*3 TT

=2*3*2*3

=36 ways

d.

Total ways of selecting = 96

With no sony = 36 ways.

Therefore, no. of ways with atleast 1 Sony gadget

= total ways- with no sony

=96-36

=60 ways

e.

Atleast 1 Sony component = 60 ways ( solved in above way)

Exactly 1 Sony component = P(Sony receiver or CDP or TT and rest)

= 1*3*2*3+2*1*2*3 + 0+2*3*2*1

= 42

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