A family is taking a picture, with everyone in the family standing in a row. In the family, there are two sets of twins. In how many ways can the 9 people in the family be arranged such that nobody is sitting next to their twin?

376320.

Step-by-step explanation:

Given:

There are two sets of twins in a family.

Total family member = 9

Solution:

Let family members = AA BB C D E F G

AA and BB are two set of twins .

First of we will find the arrangements of 5 family member   ( 9 - 4 = 5 )

No of ways 5 family member can seat =

Now, we will find the arrangements of BB.

As given that nobody is sitting next to their twin, means A twins cannot seat together.

Therefore, they can seat in these blank places given below:

......B.......B......C......... D...... E........ F........ G.......... in

Similarly,  B twins cannot seat together.

Therefore, they can seat in these blank places given below:

......A.......A......C......... D...... E........ F........ G.......... in

Total  number of arrangements of all family members =

Therefore, Total  number of arrangements of all family members is 376320.

a .4y4

hope this !