The number of ways of arranging n students in a row such that no two boys sit together and no two girls sit together is m (m > 100). If one more student is added, then number of ways of arranging as above increases by 200%. The value of n is :
The number of ways of arranging n students in a row such that no two boys sit together and no two girls sit together is m (m > 100). If one more student is added, then number of ways of arranging as above increases by 200%. The value of n is :
1). 8
2). 12
3). 9
4). 10
1 answers
If n is even, then the number of boys should be equal to number of girls, let each be a
So, n = 2a
Then the number of arrangements = 2 × a! × a!
If one more students is added, then number of arrangements = a! × (a + 1)!
But this is 200% more than the earlier
Hence, 3(2 × a! × a!) = a! × (a + 1)!
Which gives (a + 1) = 6 and a = 5
As a result n = 10
But if n is odd, then number of arrangements = a! (a + 1)!
Where, n = 2a + 1
When one student is included, number of arrangements = 2 (a + 1)! (a + 1)!
Hence, by the given condition, 2(a + 1) = 3 which is not possible.Other Questions
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