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

  • question_answer
    All possible two factors products are formed from numbers 1, 2, 3, 4, ...., 200. The number of factors out of the total obtained which are multiples of 5 is

    A) 5040

    B) 7180

    C) 8150

    D) None of these

    Correct Answer: B

    Solution :

    The total number of two factor products\[{{=}^{200}}{{C}_{2}}\]. The number of numbers from 1 to 200 which are not multiples of 5 is 160. Therefore total number of two factor products which are not multiple of 5 is\[^{160}{{C}_{2}}\]. Hence the required number of factors \[{{=}^{200}}{{C}_{2}}{{-}^{160}}{{C}_{2}}=7180\].


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