How many ways can 5 people A B C D and E can be seated around a circular table if A and B must sit together?

24
In how many different ways can five people be seated at a circular table? So the answer is 24.

How many different ways can five people a/b/c d and e sit in a row at a movie theater if?

If d and sit next to each other, they should give you the answer to this question, which is going to be 72. This is the number of ways to fight. People can be seated if D and E don’t want to sit next to each other.

How many ways 5 persons can sit at a round table if two of the persons do not sit together?

This can be done in [6 – 1]! = 120 ways. As the two person A and B can be arranged as AB or BA, total number of arrangements with the two persons next to each other is 2 x 120 = 240 ways. There are 5 x 4 x 3 x 2 x 1 = 120 ways to seat 5 people in a row.

How many ways can five people ABCD and E sit in a row at a movie theater if D and E will not sit next to each other?

And A,B,C,D,E can sit in 5!= 120 ways.

How many ways can you arrange 5 people at a table?

Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = 120. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other.

How many ways can 5 people be seated in a table?

5 people A, B, C, D and E can be seated in a round table in { (5 – 1)!} = (4!) = 24 ways. When we club A and B together; the clubbing can take place in 2 ways. And, for each such clubbing the 5 persons (virtually 4 due to clubbing of two persons), the seating arrangement can take place in (4 – 1)! = (3)! = 6 ways.

How many ways can C and D be seated together?

Similar to (i) above, the number of cases in which C and D are seated together, will be 12. Therefore the required number of ways will be 24 – 12 or 12. Example 3 In how many ways can 3 men and 3 women be seated at around table such that no two men sit together?

How many ways can you seat A and B together?

(ii) C and D never sit together. Solution (i) If we wish to seat A and B together in all arrangements, we can consider these two as one unit, along with 3 others. So, effectively we’ve to arrange 4 people in a circle, the number of ways being (4 – 1)! or 6. Let’s take a look at these arrangements:

How many ways can 5 people be clubbed together?

And, for each such clubbing the 5 persons (virtually 4 due to clubbing of two persons), the seating arrangement can take place in (4 – 1)! = (3)! = 6 ways. Therefore, the answer is in (2*6) = 12 ways.