Number of Permutations/Examples/Even Integers from 1, 2, 3, 4

Example of Number of Permutations
Let $N$ be the number of even integers which can be made using all the digits $1$, $2$, $3$ and $4$.

Then:
 * $N = 12$

Proof
An integer formed using the digits $1$, $2$, $3$ and $4$ is even it ends in $2$ or $4$.

Those $4$ digit integers ending in $2$ consist of the $3$ digits integers that can be made with $1$, $3$ and $4$

Those $4$ digit integers ending in $4$ consist of the $3$ digits integers that can be made with $1$, $2$ and $3$

From Number of Permutations, the total number of integers which can be made using $3$ different digits is $3!$.


 * $N = 2 \times 3! = 12$