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Math arrangement problem 50 points ~ ~
(1) all stand in a row, men and women stand together.

Divided into two categories: ① male left female right A3

So a * * * is 144+ 144=288 species.

(2) All stand in a row, and boys must stand together.

There are two steps: ① Bind all the boys into a whole and use A3.

(2) the bound boy as a complete person, with m-girls full row, equivalent to five people full row, with A3.

So a * * * has 6* 120=720 kinds.

(3) all stand in a row, and boys can't stand together.

There are two steps: ① Girls rank first, and A4 is used.

(2) After m-girls arranges, he gets five spaces (both ends can also be arranged, so it is empty). Three boys insert five spaces and use A5.

So a * * * has 24*60= 1440 kinds.

(4) all stand in a row, and the males and females are not adjacent.

There are two steps: ① Girls rank first, and A4 is used.

(2) m-girls lined up, there are three spaces in the middle (there can be no more people at both ends, otherwise the girls are adjacent), and three boys insert three spaces and use A3.

So a * * * has 24*6= 144 kinds.

(5) Everyone stands in a row, and there must be two people between Party A and Party B..

There are two steps: ① First, choose two people from five people other than Party A and Party B, and put them between Party A and Party B with A5.

(2) Bind the selected two people with Party A and Party B as a whole, and make a full row with the remaining three people, which is equivalent to four people making a full row, and use A4.

So a * * * has 40*24= 960 kinds.