In a certain region all license plates are composed of three letters followed by three numbers, or three numbers followed by three letters. The only restriction is that zero can never be the first ofthe three numbers if the three numbers come first. Find how many license plates are possible.

Guest Feb 11, 2018

#1**0 **

Example: 123 - ABC

The first number(1) can be chosen out of 9 numbers(1 to 9 inclusive), excluding zero.

The second number(2) can be chosen out 10 numbers(zero included)

The third number(3) can be chosed out of 10 numbers(zero included)

Then the number of ways would be: 9 x 10 x 10 =900 - provided repeats are allowed.

For the letters, provided repeats are allowed-AAA-, the the total number of the 3 letters would simply be: 26^3 =17,576

So, the total number of License Plates would be:

17,576 x 900 =**15,818,400 plates**. This is only theoretical since some 3-letter words may not be acceptable to authorities, such as "P.I .G", "GUN".....etc.

In the second case: Example: ABC - 123. Here all letters and numbers CAN be used. So then, it's straigtforward: 26^3 x 10^3 =**17,576,000 plates.**

Guest Feb 11, 2018

edited by
Guest
Feb 11, 2018

#1**0 **

Best Answer

Example: 123 - ABC

The first number(1) can be chosen out of 9 numbers(1 to 9 inclusive), excluding zero.

The second number(2) can be chosen out 10 numbers(zero included)

The third number(3) can be chosed out of 10 numbers(zero included)

Then the number of ways would be: 9 x 10 x 10 =900 - provided repeats are allowed.

For the letters, provided repeats are allowed-AAA-, the the total number of the 3 letters would simply be: 26^3 =17,576

So, the total number of License Plates would be:

17,576 x 900 =**15,818,400 plates**. This is only theoretical since some 3-letter words may not be acceptable to authorities, such as "P.I .G", "GUN".....etc.

In the second case: Example: ABC - 123. Here all letters and numbers CAN be used. So then, it's straigtforward: 26^3 x 10^3 =**17,576,000 plates.**

Guest Feb 11, 2018

edited by
Guest
Feb 11, 2018