Question
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:
Options :
4
8
10
16
Answer :
16
Solution :
There are two restrictions given :
- Q and R should be separated by one person.
- S should not be seated adjacent to Q.
Case I :
When the person 'Q' is in the starting.
Q P R S T
Q P R T S
Q T R P S
Q T R S P.
Case II :
When the person 'Q' is in second from left.
T Q P R S
P Q T R S
Case III :
When the person 'Q' is in the middle.
S T Q P R
S P Q T R
Case IV :
When the person 'R' is in the starting.
R T Q P S
R P Q T S
Case V :
When the person 'R' is in second from left.
S R P Q T
S R T Q P
Case VI :
S T R P Q
S P R T Q
P S R T Q
T S R P Q
∴ the total number of possible arrangements is 16 as per the given restrictions.
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