Six persons A, B, C, D, E, and F went to a cinema. There are six consecutive…
2025
Six persons A, B, C, D, E, and F went to a cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C, and so on. If A has taken one of the six seats, then:
B should sit adjacent to A,
C should sit adjacent to A or B,
D should sit adjacent to A, B, or C, and so on.
How many possibilities are there?
- A.
32
- B.
33
- C.
12
- D.
19
Attempted by 20 students.
Show answer & explanation
Correct answer: A
Answer: 32
Explanation: Place A first (given). The occupied seats always form one contiguous block. Each subsequent person (B, then C, then D, then E, then F) must sit adjacent to that block.
Key idea: for each arrival after A you choose whether they sit on the left end or the right end of the current block.
B: 2 choices (left end or right end)
C: 2 choices (again left or right of the block formed so far)
D: 2 choices
E: 2 choices
F: 2 choices
Total number of possibilities = 2 × 2 × 2 × 2 × 2 = 2^5 = 32.
Note: Even when the occupied block reaches a row end at some stage, that outcome is produced by a particular sequence of left/right choices earlier; counting the left/right decision at each arrival correctly counts every valid final seating.