How many different car licence plates can be constructed, if the licences contain three letters of the English alphabet followed by a three digit number, if repetition are allowed?

Explanation

(i) Total letters=26 (i.e., A,B,C, . . ,X,Y,Z)
and total digit number=10 (i.e., 0,1,2, . .,9)
If three letters on plate is represented by, then first place can be filled=26
Second place can again be filled=26 [`because` repetition are allowed]
and third place can again be filled=26

Hence, three letters can be filled`=26xx26xx26`
`=(26)^(3)` ways
and three digit numbers on plate by 999 ways.
(i.e., 001, 002, . .,999)
Hence, by the pricipal of multiplication, the required number of ways`=(26)^(3)(999)` ways
(ii) here, three letters out of 26 can be filled=`^(26)P_(3)` [`because`repetition are not allowed]
and three digit can be filled out of `10=.^(10)P_(3)` [`because` repetition are not allowed]
Hence, required number of ways`=(.^(26)P_(3))(.^(10)P_(3))` ways.