Three digits number

From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there?

Correct answer:

n =  24

Step-by-step explanation:

$$\begin{gathered} n_3\dots 2,4 \\ {n}_3=2 \\ {n}_2\dots 1,2,3,4,5\cap n_3 \\ {n}_2=5-1=4 \\ {n}_1\dots .1,2,3,4,5\cap n_2\cap n_3 \\ {n}_1=n_2-1=4-1=3 \\ n=n_1\cdot n_2\cdot n_3=3\cdot 4\cdot 2=24 \end{gathered}$$

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