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

  • question_answer
    Six '+' and four '-' signs are to placed in a straight line so that no two '-' signs come together, then the total number of ways are [IIT 1988]

    A) 15

    B) 18

    C) 35

    D) 42

    Correct Answer: C

    Solution :

    The arrangement can be make as \[2{{b}_{n}}=\frac{n}{^{n}{{C}_{0}}}+\frac{n}{^{n}{{C}_{1}}}+......+\frac{n}{^{n}{{C}_{n}}}\], the \[(-)\] signs can be put in 7 vacant (pointed) place. Hence required number of ways\[{{=}^{7}}{{C}_{4}}=35\].


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