A code word is to consist of two English alphabets followed by two distinct numbers between $1$ and $9$ . For example, $C A 23$ is a code word. How many such code words are there?

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Solution

There are in all $26$ English alphabets. We have to choose $2$ distinct alphabets.
First alphabet can be selected in $26$ ways. Second alphabet can be selected in $25$ ways. Again out of $9$ Digits ( $1$ to $9$ ), first digit can be selected in $9$ ways. second digit can be selected in $8$ ways.
Thus, the number of distinct codes
$= 26 \times 25 \times 9 \times 8$
$= 46800$

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