A code word is to consist of two distinct English letters followed by distinct numbers from 1 to 9. eg,CA23 is a code.

a) How many such codes are there?

b) How many of them end with an even integer?

(a): 
2  letters out of 26 letters can be chosen in ${}^{26}C_2 ways$.
and these two can be arranged in 2! ways
2 numbers out of 9 numbers can be chosen in ${}^{9}C_2 ways$
and theses two numbers can be arranged in 2! ways.
therefore total number of such codes = ${}^{26}C_2*2!*{}^{9}C_2*2!$
$$\begin{gathered} =\frac{26*25}{2}*2*\frac{9*8}{2}*2 \\ =26*25*72 \\ =46800 \end{gathered}$$
(b)
2 letters out of 26 letters can be chosen in ${}^{26}C_2 ways$
and it can be arranged in 2! ways.
thus first two place can be filled in ${}^{26}C_2.2!=26*25=650 ways$
if the code ends with even number 4th place can be filled with 2,4,6,8, i.e. 4 ways
and the 3rd place can be filled by 8 ways [number except the number placed in 4th place
therefore total number of codes which end with even integer
$$\begin{gathered} =650*4*8 \\ =20800 \end{gathered}$$

hope this helps you