A license 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.)

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03-10-2018
Mathematics

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A license 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.)

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Plzzzz help me ppl maths

JeanaShupp JeanaShupp · Answer 1 · 2018-10-15T07:46:09+02:00

Answer: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

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-07-04T09:11:43+02:00

The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.

Total letters = 26

Total numbers = 10

As the repetitions are allowed.

Number of ways = 26×26×26×10×10×(26+10)

N=63,273,600 Ways

P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)

The intersection of abc123 and 123abc is zero because both license plates are not possible at a time

P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)

[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]

P= 2/5616000

or

P = 1/2,808,000

Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

Learn more about the probability here:

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