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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?

1 Answer

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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)=(6!)/((6-4)!)=360.

Finally, the total possible number of IDs is:


9000*360=3240000.

Answer:


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

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