There are eight people in line, A, B, C are not adjacent, and D and E are not adjacent, how many way

8 people line up, and any two people adjacent to each other have 7a7*2=10080 kinds of queues.

There are 6a6*3a3=4320 ways to arrange any three people next to each other.

Therefore, there are at least two adjacent arrangers in A, B and C There are 10080 * 3-4320 * 2 = 21600 kinds (that is, A and B are adjacent + B and C are adjacent + A and C are adjacent - 2 times that A and B are adjacent, because this is counted 3 times that A, B and C are adjacent, and 2 times are subtracted).

Therefore, there are 8a8-21600=18720 kinds of non-adjacent arrangement methods.

Among them, there are a total of 10080 8A8*18720=4680 species adjacent to Ding and E.

Therefore, A, B and C are not adjacent, and D and E are not adjacent, and there are a total of 18720-4680 = 14040 species.

A, B, and C are not adjacent.

3 people insert 6 blanks, there are a(6,3)*a(5,5)=14400 species.

A, B, and C are not adjacent, and D, and E are "adjacent", which is regarded as one.

3 people insert 5 blanks, there are a(5,3)*a(2,2)*a(4,4)=2880 species.

So. A, B and C are not adjacent, and D and E are not adjacent.

There are 14400-2880=11520 species.

It seems that it is easy to understand after inserting a blank after A, B and C!

Ding Wu is not adjacent.

a(3,3)*a(4,2)*a(6,3)=8640 butaneous. a(2,2)*a(4,4)*c(3,1)*a(5,2)=2880

The results of both cases are summed up.

a(3,3)*a(4,2)*a(6,3)+a(2,2)*a(4,4)*c(3,1)*a(5,2)=11520

A, B and C are not adjacent, and D and E are not adjacent, and there are 5832 species.

A, B, and C-D are treated as two separate wholes. In this way, first do the arrangement of 3 units, 3!= 6 scenarios.

Among them, there are 2 situations in the different order of A and B, and C and D are also 2 types.

The above superposition calculation, there are a total of 2*2*6=24 kinds of arrangement.

a5,5=120 (not considering A and B and B A, the same as C and D) has a problem that A and B are adjacent, and B and A are also adjacent.

The same goes for propylene.

Then this is a5,5a2,2a2,2 = 480 kinds (consider A, B, and B, and the same as C-D).

A, B, and C-D are treated as two separate wholes.

Then there are 2 2 6 = 24 ways to arrange.

All six people are arranged.

a66=720

If A and B are adjacent.

is regarded as 1 person.

It is a full arrangement of 5 people, a55=120

A and B are interchangeable, so Zen Bird is 2 120 = 240, and the same is 240 kinds.

720-240-240=240 species.

A and B are adjacent and C and D are adjacent to each other are counted twice.

A and B are adjacent to each other, and C and C are adjacent.

It is equivalent to 4 people in the slow rank, a44=24

A and B are interchangeable, and C and D are also interchangeable.

So there are a total of 720-240-240+96=336 species.

6 people are all arranged a66 = 720 if A and B are adjacent, then it is regarded as 1 person is 5 people are all arranged, a55 = 120 A and B can be exchanged for each other in the morning, so it is 2 120 = 240, and the same C and D are adjacent to 240 species, 720-240-240 = 240 kinds, and A and B are adjacent and C and D are fighting each other, and the neighbors are counted twice, A and B are adjacent and C and D are adjacent to each other, which is equivalent to the 4 people in the finch arrangement, A44 = 24 A and B can be each other.

A and B are not adjacent to each other: c(5,2)*2*4!=480 B-nucleus non-adjacent arrangement: 480

A and B are adjacent and segments are vertically adjacent to B and C, and the arrangement method: 2*4!=48 A and B are not adjacent or B and C are not adjacent to each other: 6!-48 = 672 A and B are not adjacent, and B and C are not adjacent: 480 + 480-672 = 288

Total arrangement - A in the first row - B in the last row + (A in the first row and B in the last row).

There are 5 people standing in a row for a total of 5!= 120 kinds.

Among them, A and C are adjacent to the bright bridge, and there is a mountain void 2 4!= 48 species, B and C are adjacent to 48 species, and A and B are adjacent to C at the same time and have 2 3!= 12 kinds.

So the result is 120-48-48 + 12 = 36 species, 1,