Question
Thu May 17, 2012 By: Vikhyat Anand
 

In a class of 12 students, there are 3 girls. The number of different ways, in which they can be arranged in a row such that no two girls are consecutive, are

Expert Reply
Fri May 18, 2012
The 9 boys may occupy 9 places in 9P9 = 9! = 362880 ways. Since no two girls are to sit together, we may arrange the 3 girls at the 10 places shown by x marks as below:
        XBXBXBXBXBXBXBXBXBX
 
Now, the 3 girls at 10 places may be seated in:
10P3 = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604800 ways
 
Therefore, the required number of ways = (362880 x 604800) = 219469824000 ways.
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