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!

Guest Oct 19, 2019

#1**+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

power27 Oct 19, 2019

#3**+1 **

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.

Guest Oct 19, 2019

#6**+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**** **

Melody Oct 20, 2019