Oh wow — what is the value of n?

Probability Level 3

The number of ways of arranging $n$ students in a row in such a way that no two boys sit together and no two girls sit together is $m\ \ (m > 100).$ If one more student is added, then the number of ways of arranging as above increases by 200%. Find the value of $n.$

12 10 19 13

2 solutions

Parth Lohomi
Nov 24, 2014

it is directly copied from "lofoya.com" just google it! solution

this ques is given in class 11th book also

Aditya Raj - 6 years, 6 months ago

N O PROBLEM!! :)

Parth Lohomi - 6 years, 6 months ago

Aditya Raj
Nov 23, 2014

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.

The solution is too copied from " here

Parth Lohomi - 6 years, 6 months ago

If a question and solution is copied then its a minimum politeness to acknowledge that , so that other people who want to learn more can study it in detail. But i appreciate such questions and solutions.

indulal gopal - 6 years, 6 months ago

Oh wow — what is the value of n?

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