How many Licence plates can be made using either three digits followed by three uppercase English letters or three uppercase English letters followed by three digits?

Video Transcript

we want to answer how many license plates can be made using. Either three uppercase english letters followed by three digits or four uppercase english letters followed by two digits. So for the first case, Yeah. Three uppercase English letters followed by three digits. Well there are 26 English letters were choosing three of them All by three digits. There are 10 digits for choosing three. So we'll have 26 cubed times 10 cubed. So that's going to be 17 million 576,000. Then for the second case We have four English letters followed by two. Did Excuse Me? two Digits. So we'll have 26 to the power of four times 10 squared. Yeah. And that is going to be one second here. That is 45 million. 697,000. Yeah. Lastly all we need to do is add them together. So the total It's going to be 63,273,000. And so you can hear uh I missed a digit up here. That should have been for the second case Have been 45,687,600. And then the total is going to be 63,273,600. Yeah.

1 Answer

We know that Uppercase English letters = 26 

and digits =10 (0 to 9)

Three Uppercase English letters followed by Three digits:

First letter = 26 ways

Second letter = 26 ways

Third letter = 26 ways

Fourth Digit = 10 ways

Fifth Digit = 10 ways

Sixth Digit = 10 ways

Total possible ways = 26 x 26 x 26 x 10 x 10 x 10 = 17576000

Four Uppercase English letters followed by two digits:

First letter = 26 ways

Second letter = 26 ways

Third letter = 26 ways

Fourth letter = 26 ways

Fifth digit = 10 ways

Sixth digit = 10 ways

Total possible ways = 26 x 26 x 26 x 26 x 10 x 10 = 45697600

Three uppercase English letters followed by three digits or four uppercase English letters followed by two digits

   = Three Uppercase English letters followed by Three digits + Four Uppercase English letters followed by two digits

   = 17576000 + 45697600

   = 63273600

63273600 license plates can be made using either three uppercase English letters followed by three digits or four uppercase English letters followed by two digits.

How many license plates can be made using either 3 digits followed by 3 letters or 3 letters followed by 3 digits?

How many license plates can be made using either three English letters followed by three digits or four English letters followed by two digits?

How many Licence plates can be made using either two or three uppercase English letters followed by either two or three digits?

How many combinations are there with 3 numbers and 3 letters?