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Prakash

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· 1 Months ago

probaility (Question: 87370.0 )

how did 6! factorial arrive here

Question:
8 friends are sitting on 8 chairs arranged in a row. Find the probability such that all three friends  Ramesh, Jiten and Rupesh never sit together.
Options:
A) \(\cfrac{5}{8}\)
B) \(\cfrac{9}{8}\)
C) \(\cfrac{25}{28}\)
D) \(\cfrac{32}{35}\)
E) None of these
Solution:
Ans: (c) 8 friends can be seated together in 8! ways. 

Three friends Ramesh, Jiten and Rupesh always sit together by 3! X 6! ways.

  Ways in which these 3 are never sit together = 8! —(3! × 6!)

The required probability = \(\cfrac{8!- 3! \times6!}{8!}=\cfrac{6 \times50}{8!}\)  

= \(\cfrac{50}{56}=\cfrac{25}{28}\)  

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