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

  • question_answer
    \[^{14}{{C}_{4}}+\sum\limits_{j=1}^{4}{^{18-j}{{C}_{3}}}\] is equal to [EAMCET 1991]

    A) \[^{18}{{C}_{3}}\]

    B) \[^{18}{{C}_{4}}\]

    C) \[^{14}{{C}_{7}}\]

    D) None of these

    Correct Answer: B

    Solution :

    \[^{14}{{C}_{4}}{{+}^{14}}{{C}_{3}}{{+}^{15}}{{C}_{3}}{{+}^{16}}{{C}_{3}}{{+}^{17}}{{C}_{3}}{{=}^{18}}{{C}_{4}}\].


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