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

  • question_answer
    Let \[1\le m<n\le p.\]The number of subsets of the set \[A=\{1,2,3,...p\}\] having m, n as the least and the greatest elements respectively, is

    A) \[{{2}^{n-m-1}}-1\]

    B) \[{{2}^{n-m-1}}\]

    C) \[{{2}^{n-m}}\]          

    D) \[{{2}^{p-n+m-1}}\]

    Correct Answer: B

    Solution :

    [b] Between m and n, there are \[\operatorname{n} - m -1\]elements. Each subset contains m and n and for all of other n - m -1 element, there are two possibilities so, no. of subset \[={{2}^{n-m-1}}.\]


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