How many license plates are possible consisting of 4 letters followed by 2 digits, if the first letter must be a C? Repetition is allowed.

First letter must be a C

that is 1 choice, first slot is 1 choice

3 letter spaces left

we ar allowed to repeat

ther are 26 letters in the alphabet

and 10 digits

so there are 26 choices for each of the 3 letter slots and 10 choices for the last 2 slots

so the number of licence plates is 1*26*26*26*10*10=1757600 different licecne plates

Here total number of ways to put C on first position = 1

number of ways to put any letter on second position = 26

similarly for remaining positions.

total number of ways = 1*26*26*26*10*10*10*10