Permutation and Combination - Quant/Math -
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Question 4 the day:
October 24, 2002
The question for the day is from the topic of Permutation and Combination.
- There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
| (1) |
2 * 19! |
|
(2) |
18! * 18 |
|
(3) |
19! * 18 |
|
(4) |
2 * 18! |
Correct Answer - (4)
Solution:
18 people can be arranged around a circle in 17! ways. There are exactly 18 places where the two brothers can be arranged. The brothers can be arranged in 2! ways.
Therefore, the total number of ways 17! * 2 * 18 = 2 * 18!.
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