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 (let…

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asked Apr 20, 2023 141k views

1 Answer

Seanmakesgames · Answer 1 · 2023-04-24T12:50:06+0000

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:

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

Finally, the total possible number of IDs is:

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