A code word consists of three letters of the English alphabet followed 

by two digits of the decimal system. If neither letter nor digit is repeated in 

any code word, then the total number of code words, is

We have 26 letters (a to z) and 10 digits (0 to9). The

first three places can be filled with letters in ${ }^{26}{\mathrm{P}}_3$ way and the 

remaining 2 places can be filled with digits in $10P_2$ ways. Hence 

the number of ways in which the code word can be made

$=\left({ }^{26}{C}_3\times 3!\right)\times \left({ }^{10}{C}_2\times 2!\right)=1404000.$