a state issues car license plates with three letters followed by three numbers (for example, fgh831 or bbb222). how many different license plates are possible? (note that letters or numbers may repeat in the license plate. hint: use the fundamental counting rule for this question.)

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24-03-2020
Mathematics

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a state issues car license plates with three letters followed by three numbers (for example, fgh831 or bbb222). how many different license plates are possible? (note that letters or numbers may repeat in the license plate. hint: use the fundamental counting rule for this question.)

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jitumahi456 jitumahi456 · Answer 1 · 2020-03-25T05:05:42+01:00

Answer:

17576000 different License plates are possible.

Step-by-step explanation:

Here we will use repetitive permutations.

First 3 digits of the license plates have letters from a to z and next 3 digits have numbers from 0 to 9.

Now, 26 letters ( a to z ) can take 3 positions with repetition in [tex]26^{3}[/tex] ways.

And 10 numbers ( 0 to 9 ) can take 3 positions with repetition in [tex]10^{3}[/tex] ways.

So the total number of license plates that can be made = [tex]26^{3}[/tex] [tex]\times[/tex] [tex]10^{3}[/tex] = 17576 [tex]\times[/tex] 1000 = 17576000 plates.