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24 Jun 2022, 07:30
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:05) correct
35%
(02:24)
wrong
based on 226
sessions
History
Date
Time
Result
Not Attempted Yet
6 men and 6 women are seated around a table. What is the probability that three particular persons are seated together?
A. 1/55
B. 3/55
C. 2/11
D. 36/55
E. 9/11
A. 1/55
B. 3/55
C. 2/11
D. 36/55
E. 9/11
24 Jun 2022, 10:15
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Bunuel
12 people can be seated
11! ways
Treat the 3 people as one group then arrange that group with 9 other people
9! ways
Arrange the 3 people
3! ways = 6
Total ways desired
6*9!
Probability
6*9!/11! = 6/11*10 = 6/110 =
3/55
Posted from my mobile device
General Discussion
24 Jun 2022, 08:02
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Bunuel
It doesn't matter that 6 are men and 6 are women.
Let's seat Person1. Anywhere.
Person2 walks up to the table. They could sit immediately to P1's right/left or two seats to the right/left. Let's explore each of those possibilities.
Person2 sat immediately to P1's right/left:
Person3 walks up to the table. There are two seats that P3 could choose (to the right of the existing pair or to the left).
The probability of this scenario is the probability that P2 sat immediately next to P1 * the probability that P3 sat immediate to the right/left of the existing pair.
When P2 walked up to the table, there were 11 seats available and 2 that fit the criteria, so 2/11. When P3 walked up to the table, there were 10 seats available and 2 that fit the criteria, so 2/10.
2/11 * 2/10 = 4/110
Person2 sat one seat away from P1 to P1's right/left:
Person3 walks up to the table. There is one seat that P3 could choose (the one seat between P1 and P2).
The probability of this scenario is the probability that P2 sat one seat away from P1 * the probability that P3 sat between the existing pair.
When P2 walked up to the table, there were 11 seats available and 2 that fit the criteria, so 2/11. When P3 walked up to the table, there were 10 seats available and 1 that fit the criteria, so 1/10.
2/11 * 1/10 = 2/110
Either one of these scenarios wins. We need one OR the other. OR means add.
4/110 + 1/110 = 6/110 = 3/55
Answer choice B.
