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In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q

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Question: In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q and R is sitting at one of the ends, which of the following is a possible arrangement?

Options:

  1. R, P, Q, S
  2. S, R, P, Q
  3. Q, P, R, S
  4. P, S, R, Q

Correct Answer: R, P, Q, S

Solution: 

R can be at one end, and since P is next to Q, the arrangement R, P, Q, S satisfies all conditions.

In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q

Practice Questions

Q1
In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q and R is sitting at one of the ends, which of the following is a possible arrangement?
  1. R, P, Q, S
  2. S, R, P, Q
  3. Q, P, R, S
  4. P, S, R, Q

Questions & Step-by-Step Solutions

In a linear arrangement of four people P, Q, R, and S, if P is sitting next to Q and R is sitting at one of the ends, which of the following is a possible arrangement?
  • Step 1: Identify the people involved: P, Q, R, and S.
  • Step 2: Understand the conditions: P must sit next to Q, and R must be at one of the ends.
  • Step 3: Determine the possible positions for R. R can be at either the left end or the right end of the arrangement.
  • Step 4: If R is at the left end, the arrangement starts with R. We need to place P and Q next to each other.
  • Step 5: Place P next to R, which gives us R, P. Now we need to place Q next to P, resulting in R, P, Q.
  • Step 6: The only person left is S, who can be placed at the right end, giving us the arrangement R, P, Q, S.
  • Step 7: Check if this arrangement satisfies all conditions: R is at one end, and P is next to Q. It does.
  • Linear Arrangement – Understanding how to arrange items in a line based on given conditions.
  • Adjacent Positioning – Recognizing the requirement for certain items to be next to each other.
  • End Positioning – Identifying the implications of having one item at the end of a linear arrangement.
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