# 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:

A. 12

B. 8

C. 9

D. 10

**Answer: Option D **

__Solution(By Examveda Team)__

If n is even, then the number of boys should be equal to number of girls, let each be **a**.

⇒ 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

⇒ 3 × (2 × a! × a!) = a! × (a + 1)!

⇒ a + 1 = 6 and a = 5

⇒ 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)!

By the given condition, 2(a + 1) = 3, which is not possible.

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A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

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A. 7560,60,1680

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C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

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D. 9 × 8!

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