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A car license plate contains three letters followed by four digits. How many different plates can be made if no two consecutive letters can be the same, if the letters I, O and Q cannot be used, and if the number 0 cannot be used?

 

Thanks!

 Oct 19, 2019
 #1
avatar+194 
+1

26 total letters - I, O and Q = 23 letters you can use

10 total letters - 0 = 9 numbers you can use

 

There are 26 options for the first of the three letters, and 25 options for the second because it can be anything but the first letter, and 25 options for the third letter because it can't be the second letter but it can be the first letter

26*25*25=16250 ways to make the letters

 

Try to use the same logic I used to count the number of ways to make the numbers, and then multiply the number of ways to count the letters by the number of ways to count the numbers smiley

 Oct 19, 2019
 #2
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+1

Thank you so much!

Guest Oct 19, 2019
 #4
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+1

Though I'm assuming you mean 23 and 22 not 26 and 25

Guest Oct 19, 2019
 #5
avatar+194 
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Yeah I did oops

I was testing to see if you actually understood

power27  Oct 20, 2019
 #3
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23 x 22 x 21 x 9 x 9 x 9 x 9{if you allowed to repeat the numbers} =69,717,186 different license plates.

 

23 x 22 x 21 x 9 x 8 x 7 x 6{if you are not allowed to repeat the numbers} =32,133,024 different l. plates.

 Oct 19, 2019
 #6
avatar+105464 
+1

A car license plate contains three letters followed by four digits. How many different plates can be made if no two consecutive letters can be the same, if the letters I, O and Q cannot be used, and if the number 0 cannot be used?   So that is 23 letters and 9 digits to choose from.

 

Letters

First 2 the same, the third different

23*1*22 =  506 

or it could be the second 2 that are the same so times 2

1012

 

1012*9^4 = 6639732  

 Oct 20, 2019

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