Question

A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words that end with an even digit.

Answer 1

There is a total of 26 alphabets.
A code word contains 2 English alphabets.
∴ 2 alphabets can be filled in ²⁶P₂
= `(26!)/((26-2)!)=(26xx25xx24!)/(24!)` = 650 way
For a code word to end with an even integer, the digit in unit’s place should be an even number between 1 to 9 which can be filled in 4 ways.
Also, 10’s place can be filled in 8 ways.
∴ Total number of a code words = 650 × 4 × 8 = 20800 ways
∴ 20800 codewords end with an even integer.