Question

There are 12 students in a party. Five of them are girls. In how many ways can these 12 students be arranged in a row if:
there are no restrictions?
the 5 girls must be together (forming a block)?
no two girls are adjacent?

Answer 1

Heya User,

=_= I was stuck at the Qn. ^_^ 

--> No restrictions => 12 people needs to be arranged in 12 places 
                                => 12! ways ^^"

Explaination --> Either 12 can occupy first place.. either 11 at second place and so on, and finally --> 12! ways in all..

--> 5 girls together => [ 5 girls can be arranged among themselves ] *
                             [ the 8 people --> 7 guys + 1 block are to be arranged ]

=> Total no. of ways = [ 5! ] * 8! --> 8! * 5! ways

--> No two girls together --> Total no. of ways - Two of 'em together 


Note :-> Two of 'em together also counts situations like --> BGGB or BGGGB or BGGGGB cause, either way, two of 'em are together after all.

=> Two girls together = 11! * 2! ways = 2 * 11!

However, this implies that -->
 ---> No two girls together = 12! - 2*11! = 10*11! ways 

^_^ And we're done ...