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03 Jun 2026, 15:45
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E
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Difficulty:
95%
(hard)
Question Stats:
43% (01:50) correct
57%
(01:35)
wrong
based on 106
sessions
History
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Time
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Not Attempted Yet
At a circular dinner table, five couples are seated randomly. What is the probability that everybody sits adjacent to his or her partner?
A. 24/10!
B. 24/9!
C. 48/9!
D. 48/10!
E. 768/9!
A. 24/10!
B. 24/9!
C. 48/9!
D. 48/10!
E. 768/9!
03 Jun 2026, 20:25
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Treat each couple as a single block.
Total people = 10.
Total circular arrangements of 10 distinct people:
= (10 − 1)!
= 9!
Favorable arrangements:
Favorable arrangements = 4! × 25
= 24 × 32
= 768
Hence,
Probability = 768 / 9!
Answer: E. 768/9!
Total people = 10.
Total circular arrangements of 10 distinct people:
= (10 − 1)!
= 9!
Favorable arrangements:
- Arrange the 5 couple-blocks around the circle:
(5 − 1)! = 4! - Within each couple, the husband and wife can switch places:
25 ways
Favorable arrangements = 4! × 25
= 24 × 32
= 768
Hence,
Probability = 768 / 9!
Answer: E. 768/9!
BongBideshini
Joined: 25 May 2021
Last visit: 21 Sep 2026
Posts: 394
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Location: India
Concentration: Entrepreneurship, Marketing
Schools: HBS '27 Stanford '27 Wharton '27 Sloan '27
GPA: 3.8
WE:Engineering (Government)
04 Jun 2026, 02:28
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Treat each couple as a single block.
So instead of 10 people, we have 5 blocks to arrange around a circular table.
Number of circular arrangements of 5 blocks: (5-1)! = 4! = 24
Within each couple-block, the two partners can switch places: 2^5 = 32
Therefore, favorable arrangements where everybody sits adjacent to his or her partner: \(24 \times 32 = 768\)
Total ways to seat 10 distinct people around a circular table: (10-1)! = 9!
Hence, the probability that everybody sits adjacent to his or her partner = \(\frac{768}{9!}\)
Answer: E
So instead of 10 people, we have 5 blocks to arrange around a circular table.
Number of circular arrangements of 5 blocks: (5-1)! = 4! = 24
Within each couple-block, the two partners can switch places: 2^5 = 32
Therefore, favorable arrangements where everybody sits adjacent to his or her partner: \(24 \times 32 = 768\)
Total ways to seat 10 distinct people around a circular table: (10-1)! = 9!
Hence, the probability that everybody sits adjacent to his or her partner = \(\frac{768}{9!}\)
Answer: E
