Question

A state’s license plates consist of 3 letters followed by 3 numerals, and 241 letter arrangements are not allowed. How many plates can the state issue?

Answer 1

There are 26 letters. The number of ways that 3 letters can be chosen from 26 letters is 26 x 26 x 26 = 17576

Since 241 of them are not allowed, we have

15600 - 241 = 17335 arragements

There are 10 numbers. The number of ways that 3 numbers can be chosen from 10 letters is 10 x 10 x 10 = 1000

Total number of ways is

17335 * 1000

= 17335000