Question

forming license plate numbers..how many different license plate numbers can be made by using one letter followed by five digits selected from 0 through 9?

Answer 1

counting principle for this one
26 choices for the letter
\[10^5=100,000\] for the 5 digit number
you get
\[26\times 100,000\]

Answer 2

so what formula do i use?

Answer 3

and ewhy 10 to the five power?

Answer 4

The number of different permutations of n different things taken k at a time with repetitions is
\[n ^{k}\]
In your question the number of digits from 0 ~ 9 is 10 and the digits are taken 5 at a time.