JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    10 different letters of English alphabet are given. Out of these letters, words of 5 letters are formed. How many words are formed when at least one letter is repeated [UPSEAT 1999]

    A) 99748

    B) 98748

    C) 96747

    D) 97147

    Correct Answer: A

    Solution :

    Number of words of 5 letters in which letters have been repeated any times =\[{{10}^{5}}\] But number of words on taking 5 different letters out of \[10={{\,}^{10}}{{C}_{5}}=252\] \ Required number of words =\[{{10}^{5}}-252=99748\].


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