A garage door code has 5 digits. if no digits is repeated, how many codes are possible?
1 answer:
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Answer:
a) 240 ways
b) 12 ways
c) 108 ways
d) 132 ways
e) i) 0.55
ii) 0.4125
Step-by-step explanation:
Given the components:
Receiver, compound disk player, speakers, turntable.
Then a purcahser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers
Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers
Speakers: Boston, Infinity, Polk => 3 offers
Turntable: Onkyo, Sony, Teac, Technics => 4 offers
a) The number of ways one component of each type can be selected =
b) If both the receiver and compact disk are to be sony.
In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.
Thus, the number of ways components can be selected if both receiver and player are to be Sony is:
c) If none is to be Sony.
Let's exclude Sony from each component.
Receiver has 1 sony = 5 - 1 = 4
CD player has 1 Sony = 4 - 1 = 3
Speakers had 0 sony = 3 - 0 = 3
Turntable has 1 sony = 4 - 1 = 3
Therefore, the number of ways can be selected if none is to be sony:
d) If at least one sony is to be included.
Number of ways can a selection be made if at least one Sony component is to be included =
Total possible selections - possible selections without Sony
= 240 - 108
= 132 ways
e) If someone flips switches on the selection in a completely random fashion.
i) Probability of selecting at least one Sony component=
Possible selections with at least one sony / Total number of possible selections
ii) Probability of selecting exactly one sony component =
Possible selections with exactly one sony / Total number of possible selections.