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Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.
The number of distinct seating arrangements possible is
  • a)
    10  
  • b)
    8
  • c)
    4
  • d)
    16 
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Five persons P, Q, R, S and T are sitting in a row not necessarily in ...
Given information:
- 5 persons: P, Q, R, S, T
- Q and R are separated by one person
- S should not be seated adjacent to Q

To find: Number of distinct seating arrangements possible

Approach:
- We can use the concept of permutations and combinations to solve this problem.
- First, we need to find the number of ways Q and R can be seated with one person in between them.
- Then, we need to find the number of ways S can be seated such that it is not adjacent to Q.
- Finally, we can find the total number of distinct seating arrangements possible by multiplying the above two values with the number of ways the remaining two persons (P and T) can be seated.

Calculation:
- Number of ways Q and R can be seated with one person in between them = 2 (QR_P and P_QR or R_ST and T_R)
- Number of ways S can be seated such that it is not adjacent to Q = 2 (S_PT and T_PS or T_SP and P_ST)
- Number of ways the remaining two persons (P and T) can be seated = 2 (PT and TP)

Total number of distinct seating arrangements possible = 2 x 2 x 2 = 8

Therefore, the correct answer is option 'D' (16 is not a valid answer).
Free Test
Community Answer
Five persons P, Q, R, S and T are sitting in a row not necessarily in ...
Step 1 : Make proper drafting of given information 

Step 2 : Possibilities of seating arrangements. 
Case 1 :
Q P R S T  
Q T R S P 
Q P R T S 
Q T R P S 
Case 2 :
P Q T R S  
T Q P R S 
Case 3 :
S P Q T R  
S T Q P R 
Case 4 :
R P Q T S
R T Q P S 
Case 5 :
S R P Q T
S R T Q P
Case 6 :
P S R T Q
T S R P Q 
S P R T Q
S T R P Q 
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Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.The number of distinct seating arrangements possible isa)10 b)8c)4d)16Correct answer is option 'D'. Can you explain this answer?
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