Free Seating Arrangements MCQs with Answers

11. Eight friends sit around a square table, two on each side, all facing the centre. How many of them sit at a corner position?

• A. none
• B. two
• C. four
• D. eight

Explanation: With two people on each side, both occupy positions along the side rather than at the corners themselves, so no one sits at a corner. In the variant where four sit at the corners and four at the middles of the sides, the answer would be four. Reading exactly how the seats are distributed is essential before counting.

12. Five people sit in a row. If Ali does not sit at either end, how many seats could Ali occupy in a row of five?

• A. two
• B. three
• C. four
• D. five

Explanation: Excluding the two end seats leaves the three middle positions, seats 2, 3 and 4. Counting the permitted positions rather than the forbidden ones is quicker here. In a row of n seats with both ends excluded, n minus 2 places remain.

13. Three friends sit in a row. In how many different orders can they be seated?

• A. three
• B. six
• C. nine
• D. twelve

Explanation: The number of arrangements of three distinct people is 3 factorial, that is 3 multiplied by 2 multiplied by 1, which gives 6. For four people it would rise to 24, since factorials grow very quickly. Seating puzzles often turn on this counting principle.

14. In a circular arrangement of six people facing the centre, moving three places clockwise from any person brings you to

• A. the person immediately on their right
• B. the person sitting opposite them
• C. the same person
• D. the person two places to their left

Explanation: Half of six is three, so a move of three places lands directly across the circle. Moving six places would return to the starting person, since that is a full revolution. Working in fractions of the circle is quicker than counting seat by seat.

15. Four people sit in a row: M is immediately left of N, and O is immediately right of N. Where can P sit?

• A. only at the left end
• B. only at the right end
• C. at either end of the block M, N, O
• D. between M and N

Explanation: The clues lock M, N and O into a fixed block in that order, so the only free positions for P are before M or after O. P cannot break into the block, since M, N and O are described as immediately adjacent. Identifying the fixed block first is the standard opening move.

16. In a row facing north, if X is to the immediate left of Y from the reader's point of view, then from Y's point of view X is

• A. on Y's left
• B. on Y's right
• C. opposite Y
• D. behind Y

Explanation: People facing north share the reader's orientation, so left and right are the same for both, and X remains on Y's left. Had the row faced south, the directions would reverse. Establishing the facing direction before answering any left or right question is the essential habit.

17. Six students sit in a row for an examination. If two of them, A and B, must not sit next to each other, the arrangement is easiest to count by

• A. listing every possible order
• B. subtracting the arrangements where A and B are together from the total arrangements
• C. assuming A always sits first
• D. ignoring the restriction

Explanation: Counting the unwanted cases and subtracting them from the total is far quicker than enumerating what remains, and it is the standard complementary counting technique. Treating A and B as a single block gives the arrangements where they are together. The same approach handles most not adjacent conditions.

18. Five people P, Q, R, S and T sit in a row. Q is at the extreme left and T is at the extreme right. R sits immediately to the right of Q. Who could sit in the middle?

• A. Q or T
• B. P or S
• C. R only
• D. T only

Explanation: Q, R and T occupy positions one, two and five, leaving positions three and four for P and S in either order, so the middle seat is taken by whichever of them is placed third. Q and T are pinned to the ends and R to position two. Listing the fixed seats first narrows the possibilities quickly.

19. Around a circular table, the number of distinct seating arrangements of four people, counting rotations as the same, is

• A. four
• B. six
• C. twelve
• D. twenty four

Explanation: Circular arrangements of n people number n minus 1 factorial, because fixing one person removes the equivalent rotations, so for four people it is 3 factorial, which is 6. In a row the same four people could be arranged in 24 ways. The difference is exactly the factor of four rotations.

20. In a row of children, Bilal is 5th from the left and Sara is 5th from the right. If there are 12 children in total, how many children sit between Bilal and Sara?

• A. two
• B. three
• C. four
• D. one

Explanation: Sara is 5th from the right, so she is 12 minus 5 plus 1, that is the 8th from the left, while Bilal is 5th, and the children between them occupy positions 6 and 7. Converting both positions to the same reference point before subtracting is the reliable method. The count between two positions is the difference minus one.