What is the number of even six digit numbers composed of 123456, which have no duplicate numbers and 13 is not adjacent to 5

What is the number of even six digit numbers composed of 123456, which have no duplicate numbers and 13 is not adjacent to 5

solution
108
Using 123456 to form a six digit even number with no repetition
A(5)*3 = 5*4*3*2*1 *3 = 360
among
15. 51 adjacent to each other are:
C(4,1)*3*A(3)*A(2) = 4*3* 3*2*1 *2 = 144
35, 53, 144 species
153 and 351, which are adjacent to each other, have been calculated twice and added back once
C(3,1)*3 * A(2)*A(2) = 3*3*2*2 = 36
Therefore, it is necessary to use 123456 to form an even number of six digits without repetition and 13 is not adjacent to 5
360 - 144 - 144 + 36
=108 species