how many different license plates are possible if each contains 2 letters (out of the alphabet's 26 letters) followed by 5 digits (from 0 to 9) ? how many of these license plates contain no repeated letters and no repeated digits?

total number of license plates : 676000

total number of license plates with no repeated letters and no repeated digits : 468000

Step-by-step explanation:

i) the license plate is to be made up of two letters (out of 26 alphabets) followed by 5 digits (from 0 to 9).

therefore the total number of combinations for license plates when repetitions of digits and numbers are allowed will be given

26 * 26 * 10 * 10 * 10 = 676000

ii) the number of license plates containing no repeated letters and no repeated digits will be given by

26 * 25 * 10 * 9 * 8 = 468000