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

  • question_answer
    In an election the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, then the number of candidates is

    A) 7

    B) 10

    C) 8

    D) 6

    Correct Answer: C

    Solution :

    Let there are \[n\] candidates then \[^{n}{{C}_{1}}{{+}^{n}}{{C}_{2}}+......{{+}^{n}}{{C}_{n-1}}=254\]\[\Rightarrow \]\[{{2}^{n}}-2=254\] \[\Rightarrow \]\[{{2}^{n}}={{2}^{8}}\]\[\Rightarrow \]\[n=8\].


You need to login to perform this action.
You will be redirected in 3 sec spinner