JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to

    A) \[^{20}{{C}_{10}}\times {{2}^{10}}\]          

    B) \[^{20}{{C}_{10}}\times {{30}^{20}}\]

    C) \[^{20}{{C}_{10}}\times {{30}^{10}}\]        

    D) \[^{20}{{C}_{10}}\times {{2}^{20}}\]

    Correct Answer: A

    Solution :

    [a] Matches whose prediction are correct can be selected in \[^{20}{{C}_{10}}\]ways. Now each wrong prediction can be made in 2 ways. Thus, the total number of ways is \[^{20}{{C}_{10}}\times {{2}^{10}}\]

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