Latest Book Aptitude Question SOLUTION: Kiran has 8 black balls and 8 white balls. In how many ways can he arrange these balls in a row so that balls of different colours are alternate?

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(#M40021272) BOOK question Keep an EYE

Kiran has 8 black balls and 8 white balls. In how many ways can he arrange these balls in a row so that balls of different colours are alternate?

Asked In Book Abhishek (10 years ago)

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yogesh upadhyay  (5 years ago)

The 8 black balls can be arranged in
8P8 = 8! Ways ---(A)

Now we need to arrange white balls such that white balls and black balls are positioned
alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked
as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below

Explanation to Problem on Permutation

8 white balls can be arranged in the 8 positions
marked as A,B,C,D,E,F,G,H in 8P8 = 8! Ways

8 white balls can be arranged in the 8 positions
marked as B,C,D,E,F,G,H,I in 8P8 = 8! Ways

8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H
or in the 8 positions marked as B,C,D,E,F,G,H,I
in 8! + 8! = 2 × 8! Ways ---(B)

From (A) and (B),
the required number of ways = 8! × 2 × 8! = 2 × (8!)2

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