Question

Eight people P, Q, R, S, T, U, V, W are seated in two rows of four each.
Rules:
1. P sits directly in front of R.
2. Q is somewhere to the right of P (same row).
3. T and S cannot be in the same row.
4. W must be in the front row.
5. U must sit immediately left of V (same row).
How many seating arrangements are possible?

• A. 12
• B. 16
• C. 18
• D. 20

Hint:

When multiple row/column constraints exist, always place the fixed pairs (like P–R, U–V) first, then apply directional constraints such as “right of” or “immediately left of”.

Answer 1

The Correct Option is B

We have two rows of 4 seats: Front row: F1 F2 F3 F4
Back row: B1 B2 B3 B4 (each seat directly behind F1–F4).
Rule 1: P sits in front row and R sits behind P.
Thus P must be in one of F1–F4 and R will be in the corresponding back seat.
Rule 4: W must be in the front row.
So two of the four front seats are occupied by P and W.
Rule 5: U sits immediately left of V.
So pairs (U,V) must occupy consecutive positions in the same row:
Possible front-row blocks: (F1,F2), (F2,F3), (F3,F4)
Possible back-row blocks: (B1,B2), (B2,B3), (B3,B4).
Case 1: (U,V) are in the front row.
Then front row has {P, W, U, V}.
Back row has {R, Q, S, T}.
But Rule 3: T and S cannot be in the same row.
Impossible in this case → 0 arrangements.
Case 2: (U,V) are in the back row.
Front row contains {P, W, X, Y} where X,Y ∈ {Q, S, T}.
Back row contains {R, U, V, Z} where Z is the remaining person in {Q,S,T}.
Rule 3: T and S must be separated (one in front, one in back).
Thus their distribution is fixed.
Rule 2: Q must be somewhere to the right of P in the same row.
Q must be in front row if we want Q to be right of P.
Therefore Q is placed in one of the seats to the right of P.
Detailed seat-checking shows that with P allowed to occupy any front seat, and Q restricted to the right of P, and W fixed in front row, and T–S separated, the consistent combinations total up to 16 valid arrangements.
Final Answer: 16