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

  • question_answer
    The number of groups that can be made from 5 different green balls, 4 different blue balls and 3 different red balls, if at least 1 green and 1 blue ball is to be included [IIT 1974]

    A) 3700

    B) 3720

    C) 4340

    D) None of these

    Correct Answer: B

    Solution :

    At least one green ball can be selected out of 5 green balls in \[{{2}^{5}}-1\] \[i.e.\], in 31 ways. Similarly at least one blue ball can be selected from 4 blue balls in \[{{2}^{4}}-1=15\] ways. And at least one red or not red can be select in \[(n+1)\ !\] ways. Hence required number of ways = \[31\times 15\times 8=3720\].


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