Question

Each student at college has a student ID number consisting for four digits (the first digit is non zero and digits can repeat) followed by four letters A, B, C, D, E, and F (letters cannot repeat). How many different student numbers are possible?

Answer 1

First, we count the number of ways we can arrange the digits. The first number has 9 possibilities:

$1\text{ to 9,}$

the other digits have 10 possibilities each:

$0\text{ to 10.}$

Therefore, the number of ways we can arrange the digits is:

$9*10*10*10=9*10^3=9000.$

Now, for the letters, the order matters, therefore, we can use the permutation formula:

$P(6,4)=\frac{6!}{(6-4)!}=360.$

Finally, the total possible number of IDs is:

$9000*360=3240000.$

Answer:

$\begin{equation*} 3240000. \end{equation*}$