Respuesta :
11232000 different license plates are possible if letters and digits cannot be repeated
Solution:
Given that,
license plate is three letters followed by three numbers
For the first letter we have 26 ways, ( A to Z)
For the second letter we have 25 ways (Because we can't use the one letter we used for first letter )
For the third letter, we have 24 ways
The number of ways to choose our three letters is:
[tex]26 \times 25 \times 24 = 15600[/tex]
For the first number we have 10 ways (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
For the second number we have 9 ways (digist cannot be repeated )
For the third number we have 8 ways
The number of ways to choose our three numbers are:
[tex]10 \times 9 \times 8 = 720[/tex]
Therefore, total number of ways are:
[tex]15600 \times 720 = 11232000[/tex]
Thus 11232000 different license plates are possible if letters and digits cannot be repeated
There are 11232000 different license plates are possible if letters and digits cannot be repeated
Given that,license plate is three letters followed by three numbers.
we can choose first letter by 26 ways ( A to Z)
For the second letter we have only 25 choices because first letter cannot be replace again in the 26 letters
Similarly for the third letter,there are 24 number of ways
What is the meaning of arrangement?
An arrangement of items in a certain order out of which a few or all of them are taken at a time.
The number of ways to choose our three letters is we use the arrangement of three letters
Therefore we get
[tex]26 *25*24=15600 ways[/tex]
For the first number we have 10 ways (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
digits cannot be repeated
For the second number we have 9 ways
For the third number we have 8 ways
The number of ways to choose our three numbers are
[tex]10*9*8=720 ways[/tex]
Therefore, total number of ways are
[tex]15600*720=11232000 ways[/tex]
Thus 11232000 different license plates are possible if letters and digits cannot be repeated.
To learn more about the arrangement visit:
https://brainly.com/question/6032811
