2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Permutations and Combinations

JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

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

    A) 166674

    B) 169194

    C) 166680

    D) 181434

    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
    \[=\frac{9!}{2!}-\left( 7!+7!+\frac{7!}{2} \right)+3\times 5!-3!=169194.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner