Arranging Persons in a Row with Constraints

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In summary, the number of ways in which 4 persons can be arranged in a row such that each person does not follow the person immediately before them is 8. This is calculated by considering all possible arrangements where P1 is in the first position and then multiplying by 2, since P1 can also be in the second position. However, the assumption that P1 is in the first position may be incorrect, leading to a different solution.
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utkarshakash
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Homework Statement


The number of ways in which 4 persons P1,P2,P3,P4 can be arranged in a row such that P2 does not follow P1, P3 does not follow P2 and P4 does not follow P3 is


The Attempt at a Solution



Let us assume that P1 occupies the first position. So, the next position can be occupied by P3 or P4. Thus, there are 2 ways by which the required arrangement can be made, P1 occupying the first seat. Since there are 4 persons, we have 2*4=8 ways by which the persons can be seated according to the given condition. But this is not correct. I can't figure out where I'm going wrong.
 
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  • #2
utkarshakash said:

Homework Statement


The number of ways in which 4 persons P1,P2,P3,P4 can be arranged in a row such that P2 does not follow P1, P3 does not follow P2 and P4 does not follow P3 is

What does it mean for one person to "not follow" another when they are seated in a row?
 
  • #3
LCKurtz said:
What does it mean for one person to "not follow" another when they are seated in a row?

I'm assuming that they should not be seated next to each other.
 
  • #4
utkarshakash said:
I'm assuming that they should not be seated next to each other.
I would interpret it as meaning they are not adjacent in a specific order. I.e. if we regard the leftmost position as the first position then P2 cannot be immediately to the right of P1, etc. P2-P1-P4-P3 would be valid.
This means you cannot assume P1 is in first position.
The only other interpretation of those words that seems reasonable to me is that P2 cannot be anywhere to the right of P1, etc. But then the problem becomes trivial.
 

1. What is the probability of persons sitting in a row?

The probability of persons sitting in a row depends on the total number of persons and the arrangement of seating. If the seating arrangement is random, then the probability would be 1/n, where n is the total number of persons.

2. How many ways can persons be seated in a row?

The number of ways persons can be seated in a row is calculated using the factorial formula, n!, where n is the number of persons. For example, if there are 4 persons, the number of ways they can be seated is 4! = 24 ways.

3. How do you determine the number of persons in a row?

The number of persons in a row can be determined by counting the total number of seats in the row or by using the factorial formula, n!, where n is the number of ways persons can be seated in the row.

4. What is the difference between a row and a column in seating?

A row is a horizontal arrangement of seats, while a column is a vertical arrangement of seats. In a row, persons are seated next to each other, while in a column, persons are seated one behind the other.

5. How does the arrangement of persons in a row affect communication?

The arrangement of persons in a row can affect communication depending on factors such as distance between persons, line of sight, and physical barriers. If persons are seated too far apart or if there are obstructions, it can hinder communication. However, if persons are seated closer together and have a clear line of sight, it can facilitate communication.

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