JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    How many numbers can be formed from the digits 1, 2, 3, 4 when the repetition is not allowed

    A) \[^{4}{{P}_{4}}\]

    B) \[^{4}{{P}_{3}}\]

    C) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}\]

    D) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\]

    Correct Answer: D

    Solution :

    Number of 1 digit numbers \[{{=}^{4}}{{P}_{1}}\] Number of 2 digit numbers \[{{=}^{4}}{{P}_{2}}\] Number of 3 digit numbers \[{{=}^{4}}{{P}_{3}}\] Number of 4 digit numbers \[{{=}^{4}}{{P}_{4}}\] Hence the required number of ways \[{{=}^{4}}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\].

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