Permutations And Combinations Question 270

Question: In how many ways $ n $ books can be arranged in a row so that two specified books are not together

Options:

A) $ n!-(n-2)! $

B) $ (n-1)!(n-2) $

C) $ n!-2(n-1) $

D) $ (n-2)n! $

Show Answer

Answer:

Correct Answer: B

Solution:

  • Total number of arrangements of $ n $ books $ ^{n}P_n\times 1\ !=86400 $ . If two specified books always together then number of ways $ =(n-1)\ !\ \times 2 $ Hence required number of ways $ =n\ !-(n-1)\ !\ \times 2 $ $ =n(n-1)\ !\ -(n-1)\ \times 2=(n-1)\ !\ (n-2) $ .

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