Alicense plate has six characters. three characters are letters, two characters are numbers (0-9), and one character is a letter or a number. the letters and numbers can repeat. note: there are 26 letters in the alphabet. how many different license plates can be made? answer plates what is the probability of getting a plate with abc123 or 123abc? p(abc123 or 123abc) = answer (enter as a reduced fraction using / for the fraction bar.)

1)Number of different license plates can be made =17576×100×260=456976000

2)Probability of getting a plate with abc123 or 123 abc=0.0000004

Given that :-A license plate has six characters.

As three characters are letters ∴ ways of these 3 letters into the plate with repetition = 26×26×26=17576 ways

and  two characters are numbers (0-9 - total 10 characters)∴ways of these 2 numbers into the plate with repetition=10×10 =100 ways

and one character is a letter or a number=26×10=260

So number of different license plates can be made =17576×100×260=456976000

Now Probability of getting a plate with abc123 or 123 abc

=P(abc123 or 123abc)=P(abc123)+P(123abc)-P(abc123)×P(123abc)=1/456976000+1/456976000-1/456976000×1/456976000

=1/456976000(1+1-1/456976000)

=1/456976000(2-0.0000002)=2/456976000=0.0000004

Probability of getting a plate with abc123 or 123 abc=0.0000004

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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