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.
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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