SATHEE: Permutations And Combinations Question 353

Permutations And Combinations Question 353

Question: The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ?HIN? nor ?DUS? nor ?TAN? appears, are

Options:

A) 166674

B) 169194

C) 166680

D) 181434

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Total number of permutations $ =\frac{9!}{2!} $ Number of those containing $ ‘HIN’ $ $ =7! $ Number of those containing ?DUS? $ =\frac{7!}{2!} $ Number of those containing ?TAN? $ =7! $ Number of those containing ?HIN? and ?DUS? $ =5! $ Number of those containing ?HIN? and ?TAN? $ =5! $ Number of those containing ?TAN? and ?DUS? $ =5! $ Number of those containing ?HIN? and ?DUS? and ?TAN?=3! Required number $ =\frac{9!}{2!}-( 7!+7!+\frac{7!}{2} )+3\times 5!-3!=169194. $

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Permutations And Combinations Question 353

Question: The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ?HIN? nor ?DUS? nor ?TAN? appears, are

Options:

Answer:

Solution:

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