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

  • question_answer
    Ten different letters of an alphabet are given, words with five letters are formed form these given letters. Then the number of words which have at least one letter repeated is

    A) 69760

    B) 30240

    C) 99784

    D) None of these

    Correct Answer: A

    Solution :

    [a] Total number of words that can be formed \[={{10}^{5}}.\] Number of words in which no letter is repeated \[{{=}^{10}}{{P}_{5}}.\]So, number of words in which at least one letter is repeated \[={{10}^{5}}{{-}^{10}}{{P}_{5}}=69760.\]


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