There are 2 brothers among a group of 20 persons. The number of ways the group can be arranged around a circle so that there is exactly one person between the two brothers is
A
2×17!
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B
18!×18
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C
2×18!
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D
2×17!×17
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Solution
The correct option is C2×18! The person who sits in between the two brothers can be selected in18C1=18 ways.
Consider the two brothers and the person in between the brothers as one unit.
Then the number of distinct units are 20−3+1=18
Now the brothers can be arranged on either side of the person in 2! ways.
Therefore, the total number of ways =18(18−1)!×2 =2×18!