Question

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

Answer 1

The number of permutations of n different things taken k at a time with repetitions is\[n ^{k}\]
The number of permutations of letters is 26^3.
The number of permutations of the 10 digits from 0 to 9 taken 4 at a time is 10^4.
Each of the permutations of letters can be taken with each of the permutations of digits. Therefore the total possible number of licence plates is
\[26^{3}\times 10^{4}\]